More Linear Relationships

Let’s explore some more relationships between two variables.

6.1: Growing

Look for a growing pattern. Describe the pattern you see.

3 diagrams. diagram 1, 1 yellow, 3 blue, 1 red. diagram 2, 4 yellow, 6 blue, 2 red. diagram 3, 9 yellw, 9 blue, 3 red.

If your pattern continues growing in the same way, how many tiles of each color will be in the 4th and 5th diagram? The 10th diagram?

How many tiles of each color will be in the \(n\) th diagram? Be prepared to explain how your reasoning.

6.2: Slopes, Vertical Intercepts, and Graphs

Your teacher will give you 6 cards describing different situations and 6 cards with graphs.

  • Match each situation to a graph.

Pick one proportional relationship and one non-proportional relationship and answer the following questions about them.

  • How can you find the slope from the graph? Explain or show your reasoning.
  • Explain what the slope means in the situation.
  • Find the point where the line crosses the vertical axis. What does that point tell you about the situation?

6.3: Summer Reading

Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days.

After day 1, Lin reaches page 70, which matches the point \((1,70)\) she made on her graph. After day 4, Lin reaches page 190, which does not match the point \((4,160)\) she made on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.

Graph of line. Points plotted on line include 1 comma 70 and 4 comma 160.

  • Sketch a line showing Lin's original plan on the axes.
  • What does the vertical intercept mean in this situation? How do the vertical intercepts of the two lines compare?
  • What does the slope mean in this situation? How do the slopes of the two lines compare?

Jada's grandparents started a savings account for her in 2010. The table shows the amount in the account each year.

If this relationship is graphed with the year on the horizontal axis and the amount in dollars on the vertical axis, what is the vertical intercept? What does it mean in this context?

At the start of summer break, Jada and Lin decide to save some of the money they earn helping out their neighbors to use during the school year. Jada starts by putting \$20 into a savings jar in her room and plans to save \$10 a week. Lin starts by putting \$10 into a savings jar in her room plans to save \$20 a week. Here are graphs of how much money they will save after 10 weeks if they each follow their plans:

Graph of 2 lines in quadrant 1. Horizontal axis, time in weeks, scale 0 to 12, by 1’s. Vertical axis, amount saved in dollars, scale 0 to 100, by 20’s.

Description: <p>Graph of 2 lines in quadrant 1. Horizontal axis, time in weeks, scale 0 to 12, by 1’s. Vertical axis, amount saved in dollars, scale 0 to 100, by 20’s. Lin line, y intercept = 10. Slope = 20. Jada line, y intercept = 20, slope= 10.</p>

The value where a line intersects the vertical axis is called the vertical intercept . When the vertical axis is labeled with a variable like \(y\) , this value is also often called the \(y\) -intercept . Jada's graph has a vertical intercept of \$20 while Lin's graph has a vertical intercept of \$10. These values reflect the amount of money they each started with. At 1 week they will have saved the same amount, \$30. But after week 1, Lin is saving more money per week (so she has a larger rate of change), so she will end up saving more money over the summer if they each follow their plans.

Glossary Entries

A linear relationship between two quantities means they are related like this: When one quantity changes by a certain amount, the other quantity always changes by a set amount. In a linear relationship, one quantity has a constant rate of change with respect to the other.

The relationship is called linear because its graph is a line.

The graph shows a relationship between number of days and number of pages read.

When the number of days increases by 2, the number of pages read always increases by 60. The rate of change is constant, 30 pages per day, so the relationship is linear.

The vertical intercept is the point where the graph of a line crosses the vertical axis.

The vertical intercept of this line is \((0,\text-6)\) or just -6.

A graph of a line with a vertical intercept of -6

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3.2.2: More Linear Relationships

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  • Illustrative Mathematics
  • OpenUp Resources

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Let's explore some more relationships between two variables.

Exercise \(\PageIndex{1}\): Growing

Look for a growing pattern. Describe the pattern you see.

clipboard_e5f04644822caaf15d1c545744db0394d.png

  • If your pattern continues growing in the same way, how many tiles of each color will be in the 4th and 5th diagram? The 10th diagram?
  • How many tiles of each color will be in the \(n\)th diagram? Be prepared to explain how your reasoning.

Exercise \(\PageIndex{2}\): Slopes, Vertical Intercepts, and Graphs

Your teacher will give you 6 cards describing different situations and 6 cards with graphs.

  • Match each situation to a graph.
  • How can you find the slope from the graph? Explain or show your reasoning.
  • Explain what the slope means in the situation.
  • Find the point where the line crosses the vertical axis. What does that point tell you about the situation?

Exercise \(\PageIndex{3}\): Summer Reading

Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days.

After day 1, Lin reaches page 70, which matches the point \((1,70)\) she made on her graph. After day 4, Lin reaches page 190, which does not match the point \((4,160)\) she made on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.

clipboard_e1268f4852ebf0241363a42845449c7be.png

  • Sketch a line showing Lin's original plan on the axes.
  • What does the vertical intercept mean in this situation? How do the vertical intercepts of the two lines compare?
  • What does the slope mean in this situation? How do the slopes of the two lines compare?

Are you ready for more?

Jada's grandparents started a savings account for her in 2010. The table shows the amount in the account each year.

If this relationship is graphed with the year on the horizontal axis and the amount in dollars on the vertical axis, what is the vertical intercept? What does it mean in this context?

At the start of summer break, Jada and Lin decide to save some of the money they earn helping out their neighbors to use during the school year. Jada starts by putting $20 into a savings jar in her room and plans to save $10 a week. Lin starts by putting $10 into a savings jar in her room plans to save $20 a week. Here are graphs of how much money they will save after 10 weeks if they each follow their plans:

clipboard_e2d0212490da55946dac981334986540a.png

The value where a line intersects the vertical axis is called the vertical intercept . When the vertical axis is labeled with a variable like \(y\), this value is also often called the \(y\) -intercept . Jada's graph has a vertical intercept of $20 while Lin's graph has a vertical intercept of $10. These values reflect the amount of money they each started with. At 1 week they will have saved the same amount, $30. But after week 1, Lin is saving more money per week (so she has a larger rate of change), so she will end up saving more money over the summer if they each follow their plans.

Glossary Entries

Definition: Linear Relationship

A linear relationship between two quantities means they are related like this: When one quantity changes by a certain amount, the other quantity always changes by a set amount. In a linear relationship, one quantity has a constant rate of change with respect to the other.

The relationship is called linear because its graph is a line.

The graph shows a relationship between number of days and number of pages read.

When the number of days increases by 2, the number of pages read always increases by 60. The rate of change is constant, 30 pages per day, so the relationship is linear.

clipboard_e4d1fd0f0259d7198073a02ce75a7303d.png

Definition: Vertical Intercept

The vertical intercept is the point where the graph of a line crosses the vertical axis.

The vertical intercept of this line is \((0,-6)\) or just -6.

clipboard_ea9fc8ec38e43e70ee19cfa3df0f6c2ef.png

Exercise \(\PageIndex{4}\)

Explain what the slope and intercept mean in each situation.

  • A graph represents the perimeter, \(y\), in units, for an equilateral triangle with side length \(x\) units. The slope of the line is 3 and the \(y\)-intercept is 0.
  • The amount of money, \(y\), in a cash box after \(x\) tickets are purchased for carnival games. The slope of the line is \(\frac{1}{4}\) and the \(y\)-intercept is 8.
  • The number of chapters read, \(y\), after \(x\) days. The slope of the line is \(\frac{5}{4}\) and the \(y\)-intercept is 2.
  • The graph shows the cost in dollars, \(y\), of a muffin delivery and the number of muffins, \(x\), ordered. The slope of the line is 2 and the \(y\)-intercept is 3.

Exercise \(\PageIndex{5}\)

Customers at the gym pay a membership fee to join and then a fee for each class they attend. Here is a graph that represents the situation.

  • What does the slope of the line shown by the points mean in this situation?
  • What does the vertical intercept mean in this situation?

clipboard_ec5c39cf04a95d9ecc06774c44209f0a4.png

Exercise \(\PageIndex{6}\)

The graph shows the relationship between the number of cups of flour and the number of cups of sugar in Lin’s favorite brownie recipe.

clipboard_e97dbc6843052f7dda149d25de3b901c5.png

The table shows the amounts of flour and sugar needed for Noah's favorite brownie recipe.

  • Noah and Lin buy a 12-cup bag of sugar and divide it evenly to make their recipes. If they each use all their sugar, how much flour do they each need?
  • Noah and Lin buy a 10-cup bag of flour and divide it evenly to make their recipes. If they each use all their flour, how much sugar do they each need?

(From Unit 3.1.4)

Illustrative Mathematics Grade 8, Unit 3, Lesson 6: More Linear Relationships

Learning Targets:

  • I can interpret the vertical intercept of a graph of a real-world situation.
  • I can match graphs to the real-world situations they represent by identifying the slope and the vertical intercept.

Related Pages Illustrative Math Grade 8

Lesson 6: More Linear Relationships

Let’s explore some more relationships between two variables.

Illustrative Math Unit 8.3, Lesson 6 (printable worksheets)

Lesson 6 Summary

Linear Relationships

Lesson 6.1 Growing

Look for a growing pattern. Describe the pattern you see.

  • If your pattern continues growing in the same way, how many tiles of each color will be in the 4th and 5th diagram? The 10th diagram?
  • How many tiles of each color will be in the nth diagram? Be prepared to explain how your reasoning.

Lesson 6.2 Slopes, Vertical Intercepts, and Graphs

Your teacher will give you 6 cards describing different situations and 6 cards with graphs.

  • Match each situation to a graph.
  • Pick one proportional relationship and one non-proportional relationship and answer the following questions about them. a. How can you find the slope from the graph? Explain or show your reasoning. b. Explain what the slope means in the situation. c. Find the point where the line crosses the vertical axis. What does that point tell you about the situation?

Lesson 6.3 Summer Reading

Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she’ll read over the next few days. After day 1, Lin reaches page 70, which matches the point (1,70) she made on her graph. After day 4, Lin reaches page 190, which does not match the point (4,160) she made on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.

  • Sketch a line showing Lin’s original plan on the axes.
  • What does the vertical intercept mean in this situation? How do the vertical intercepts of the two lines compare?
  • What does the slope mean in this situation? How do the slopes of the two lines compare?

Are you ready for more?

The vertical intercept is 600. It was the starting amount in the year 2010.

Lesson 6 Practice Problems

  • Explain what the slope and intercept mean in each situation. a. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0. b. The amount of money, y, in a cash box after x tickets are purchased for carnival games. The slope of the line is 1/4 and the y-intercept is 8. c. The number of chapters read, y, after x days. The slope of the line is 5/4 and the y-intercept is 2. d. The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.
  • The graph shows the relationship between the number of cups of flour and the number of cups of sugar in Lin’s favorite brownie recipe. The table shows the amounts of flour and sugar needed for Noah’s favorite brownie recipe. a. Noah and Lin buy a 12-cup bag of sugar and divide it evenly to make their recipes. If they each use all their sugar, how much flour do they each need? b. Noah and Lin buy a 10-cup bag of flour and divide it evenly to make their recipes. If they each use all their flour, how much sugar do they each need?
  • Customers at the gym pay a membership fee to join and then a fee for each class they attend. Here is a graph that represents the situation. a. What does the slope of the line shown by the points mean in this situation? b. What does the vertical intercept mean in this situation?

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics .

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Tips for Creating Summer Reading Assessment Ideas (Plus 3 Fun Ideas!)

Many teachers assign summer reading. However, summer reading can be difficult for students who lack time management skills, motivation, or even the literacy skills necessary to complete the work. 

For this reason, summer reading assessment can also be challenging, as students can disengage from the material and Google answers to questions or read summaries instead of reading the book.

Despite its challenges, summer reading assignments can still have value in the English Language Arts classroom. We need to look at how we assess summer reading -- making reading enjoyable rather than a drag for everyone. 

tips and ideas for summer reading assessments for middle and high school

Here's how to get the most out of your summer reading assignments:

What is a summer reading assessment?

I like to look at assessments as three prongs of the same concept: Accountability Assessments, Critical Thinking Assessments, and Creative Assessments. Each one is slightly different from the other, but all equally valuable assessment tools. The three prongs overlap more often than not. 

Each one has value, and they work better when you vary the types of assessments you use, and you do not rely on just one type too much. Each type of assessment requires students to think on different levels of Bloom’s Taxonomy. 

What are the three types of Reading Assessments?

Accountability Assessments

These are traditional tests and assignments that aim to keep students accountable to complete the reading. Think: study guides, reading guides, and end-of-the-novel tests and quizzes. These are not to be confused with state or district-level standardized testing. 

Critical Thinking Assessments

These are higher-level critical thinking assignments that encourage students to analyze, synthesize, and evaluate the summer reading. There are a variety of ways to format this type of assessment. Think: small group discussions such as a Socratic Seminar, or a literary analysis paragraph writing where students identify and analyze the purpose and effectiveness of an author’s use of figurative language and other literary elements. 

Creative Assessments

These are projects and other assignments that require accountability and critical thinking, but also include creativity and fun. Think of posters, interpretive projects, video creation, podcast creation, etc. 

Creative Reading Assessments

Creative Assessments are by far the most engaging and valuable to address the unique challenges of summer reading. Innovative summer reading assessments can make all the difference for kids who may not have otherwise completed the task. Having relevant, engaging, and interesting assessments will not only increase the chances that students will do the summer reading, but it will also be a great introduction to your class in the fall!

Below are some ideas for creative reading assessments for your summer reading assignments. 

Snap Chat Conversation

Snapchat has been around for a while, and the way teens use it, it doesn’t seem to be going away anytime soon. Why not capitalize on that? (Kids can still keep their streaks going, too!) For this project, have students create a series of snaps that show characters interacting with each other. They can save these snaps as images, upload them to Google Slides or PowerPoint and either just turn them in, or present them. Better yet, have that student select a partner to read out loud the snaps! 

Character Awards

To freshen up your summer reading assignment, try having students create unique and interesting awards for the characters. This is a good way for students to recall information and analyze character development at the same time. Ask students to come up with the award and the reason why that character earned it. For example, Boo Radley could receive the award for “Hero Least Likely to Need Sunscreen” for his valiant rescue of the Finch children after years of reclusive behavior that goes back to his childhood. To make it more fun and engaging, another student could come up to receive the award, in character, and give an acceptance speech with references from the text. 

Character Letters of Recommendation

Students, especially juniors and seniors, are familiar with the art of asking and receiving a letter of recommendation. But they haven’t had the experience of writing one! With this type of assessment, students can get into the counselor/teacher character and write a letter praising, thinly sugarcoating, or even criticizing a character from the reading. Clear references to the text should be used to support your reasoning for recommending, or even not recommending, a character. 

These are just three different ideas to assess your summer reading assignments for middle or high school in a creative way. What creative ways do you use to assess summer reading? We'd love to hear!

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Much Ado About Teaching

Summer reading in ap lit..

lin has a summer reading assignment

A few years ago I revamped my summer reading assignment.

It marked an important departure for me. It was a significant step in my growth as a teacher. I’ll explain why, but first I want to share what I have done in years past.

THE OLD SUMMER READING ASSIGNMENT

My summer assignment has gone through different iterations over the years, but the gist of it has always been that the students had to read two books — How to Read Literature Like a Professor: A Lively and Entertaining Guide to Reading Between the Lines and 1984 — and develop an outline for each. There are many versions of this assignment online. Its probably where I first developed the idea. I must have Googled “ How to Read Literature Like a Professor summer assignment.” A bunch of results came up, and seeing that a lot of other teachers paired Thomas C. Foster’s work with another novel probably validated its worth in my mind.

I liked that both books were accessible and my students could find help online if they needed it.

I liked that I was introducing my students to good literature without ruining their summer with dense texts and mountains of work.

I liked that when students returned from school I could assess them by asking them to apply a chapter from How to Read Literature Like a Professor to 1984 .

I liked that I was doing something to prevent the summer slide.

THE PROBLEM WITH THE OLD ASSIGNMENT

There was nothing pedagogically wrong with my old summer reading assignment. But there were certain things about it that had bothered me over the years:

  • Students can easily find summaries of How to Read Literature Like a Professor online ( like this link) .
  • Many of my students are not readers of classic literature on their own. In spite of its cheeky humor and tone, they did not have the awareness of texts mentioned in How to Read Literature to fully appreciate the references.
  • Students felt that How to Read Literature Like a Professor simplified the process of reading, reducing everything to either a symbol or an allusion.
  • The assignment was not thoroughly thought through. It was too simplistic. Basically I was asking students to read and outline. I felt like I was simply following what others were doing without making this assignment a true reflection of my teaching and my goals.
  • There wasn’t much feedback I could provide on an outline and consequently little room for growth.

THE GOALS OF SUMMER ASSIGNMENTS

I believe that when students are faced with low-rigor tasks, they create low achievement even when students do well on these tasks. In addition, such tasks contribute to the boredom students so often complain about when they spend too many hours on work that is routine and bland, often centered on discrete skills.

Outlining a text is a low-rigor task. It requires little skill beside extrapolation and summarization.

I want my summer assignments to have what I believe are the three principles of an effective assignment:

1. Effective assignments provide clear expectations about what should be completed, how it should be completed, and why the assignment is important.

I needed to rethink the final part of that criteria. While the original assignment provided clear expectations and walked students through the steps to be completed, it never explained why the assignment was important. When there is no value attached to an assignment, the work can feel like busy work.

Assignment-making requires teachers to clarify what learning is demonstrated and how it can be demonstrated. I needed to answer questions about purpose and relevance: “Why are my students doing this? What greater good will result from this work? As well as, are there significant concepts connected to the curriculum?”

2. Effective assignments are formative, providing feedback that allows teachers to adjust their instruction and scaffold learning.

I also needed to understand how my teaching can be informed by what the students completed. This is where the outlines of the prior assignment failed to be valuable. I was learning nothing about my students nor anything about their thinking.

With the new summer assignment adjustments would I make based on the work that students produced? What was I learning about their reading skills or their writing skills?

Good assignments, whether in the summer or during the school year, should inform instruction, giving teachers a chance to assess skills and modify instruction accordingly.

3. Effective assignments set high expectations and provide pathways to achieve those expectations.

I want the new assignment to communicate high expectations for critical thinking and levels of analysis. I want my students to be challenged no matter what skill sets or content background they bring into the course.

WHAT MY STUDENTS ARE DOING INSTEAD

  • I want my students to have a summer experience that is not punitive but is preparatory. I don’t want to punish them with mountains of work or use a summer assignment as a gatekeeper for the class. I want to set a foundation for the enjoyment that comes from reading, thinking, and writing creatively and analytically.
  • I want my students to see that great ideas can be expressed in a variety of formats. Therefore, they will read blog articles, watch YouTube videos, and read poems as well as a novel.
  • I want them to learn from readers, writers, and thinkers that I admire. I’m not just handing them books and asking them to read them, I want them to observe how others analyze and how others approach the act of writing.  These pieces have the levels of analysis that will promote high expectations for my students.
  • I want them to choose the novel they read, not have one assigned to them.
  • I want them to have a space of their own creation (their StudyTee Notes) where they will respond to each text that they encounter in thoughtful and diverse ways.

THE SUMMER READING TEXTS

  • StudyTee’s Note-Taking Method
  • The NerdWriter Analyzes Edward Hopper’s “Nighthawks”
  • Leo Babauta’s Why I Read (+ a Dozen Book Recommendations)
  • Any novel on this list or this one
  • Poetry Foundation’s Poem of the Day

Download the Summer Reading Assignments for Susan Barber and Brian Sztabnik

Concluding thoughts.

I know that I am asking my students to complete somewhat unorthodox summer assignments. They are not being handed a textbook or a stack of novels and asked to complete a series of study guide questions or outlines. There comes a point in a teacher’s career when he or she stops doing things just because everyone else is doing them and strikes out on his or her own path.

And this has been that moment for me.

Instead, I am giving them models of critical thinkers. I am exposing them to a variety of texts across a span of genres. I am giving them the power to choose the novel and poems that they want to read. And it will have clear expectations, an understanding of why each component of the assignment is important, a chance for me to gain formative feedback, and high expectations for success.

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Brian Sztabnik is just a man trying to do good in and out of the classroom. He was a 2018 finalist for NY Teacher of the Year, a former College Board advisor for AP Lit, and an award-winning basketball coach.

lin has a summer reading assignment

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Summer Reading

NEST+m is a community of readers. Each summer, our students receive grade-specific reading assignments. Please see the information below for Lower, Middle and Upper Grades summer reading assignments. All books have been carefully chosen by our ELA teachers.

Before starting your assignment, please read the important information below:

“Books are sometimes windows , offering views of worlds that may be real or imagined, familiar or strange. Readers have only to [look] through in imagination to become part of whatever world has been created and recreated by the author . 

[A book] can also be a mirror. Literature transforms human experience and reflects it back to us, and in that reflection we can see our own lives and experiences as part of the larger human experience . 

Reading, then, becomes a means of self-affirmation , and readers often seek their mirrors in books… 

[We] need books that will help them understand the multicultural nature of the world they live in, and their place as a member of just one group, as well as their connections to all other humans.”  

“ Mirrors, Windows, and Sliding Glass Doors ” (1990)

lin has a summer reading assignment

Upper Grades 9-12

Summer 2024 Assignment is still to be announced!

Last year's assignment:

Please see the Grades 9-12 Summer Reading Assignment

  • Grade 9 reading list
  • Grade 10 reading list
  • Grades 11 & 12 reading list

Hard cover books in a stack.

Middle Grades 6-8

Please see the Summer Reading assignments for 2023 :

  • 7th & 8th Grade

Summer reading assignments are due during the first week of ELA class. 

Old books opened and stacked in a pile.

Lower Grades K-5

Please see our Summer 2023 Reading Assignments :

  • Kindergarten does not have a Summer Reading assignment
  • Grades 1 & 2
  • Grades 3, 4 & 5

Get real time school updates on your mobile device with eChalk Notify .

Connect with code 8UTD2R to get instant alerts or log in with your eChalk user account for the latest updates from all your classes and groups.

Get it on Google Play

More Linear Relationships

Let’s explore some more relationships between two variables.

6.1: Growing

Look for a growing pattern. Describe the pattern you see.

3 diagrams. diagram 1, 1 yellow, 3 blue, 1 red. diagram 2, 4 yellow, 6 blue, 2 red. diagram 3, 9 yellw, 9 blue, 3 red.

If your pattern continues growing in the same way, how many tiles of each color will be in the 4th and 5th diagram? The 10th diagram?

How many tiles of each color will be in the \(n\) th diagram? Be prepared to explain how your reasoning.

6.2: Slopes, Vertical Intercepts, and Graphs

Your teacher will give you 6 cards describing different situations and 6 cards with graphs.

  • Match each situation to a graph.

Pick one proportional relationship and one non-proportional relationship and answer the following questions about them.

  • How can you find the slope from the graph? Explain or show your reasoning.
  • Explain what the slope means in the situation.
  • Find the point where the line crosses the vertical axis. What does that point tell you about the situation?

6.3: Summer Reading

Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days.

After day 1, Lin reaches page 70, which matches the point \((1,70)\) she made on her graph. After day 4, Lin reaches page 190, which does not match the point \((4,160)\) she made on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.

Graph of line. Points plotted on line include 1 comma 70 and 4 comma 160.

  • Sketch a line showing Lin's original plan on the axes.
  • What does the vertical intercept mean in this situation? How do the vertical intercepts of the two lines compare?
  • What does the slope mean in this situation? How do the slopes of the two lines compare?

Jada's grandparents started a savings account for her in 2010. The table shows the amount in the account each year.

If this relationship is graphed with the year on the horizontal axis and the amount in dollars on the vertical axis, what is the vertical intercept? What does it mean in this context?

At the start of summer break, Jada and Lin decide to save some of the money they earn helping out their neighbors to use during the school year. Jada starts by putting \$20 into a savings jar in her room and plans to save \$10 a week. Lin starts by putting \$10 into a savings jar in her room plans to save \$20 a week. Here are graphs of how much money they will save after 10 weeks if they each follow their plans:

Graph of 2 lines in quadrant 1. Horizontal axis, time in weeks, scale 0 to 12, by 1’s. Vertical axis, amount saved in dollars, scale 0 to 100, by 20’s.

Description: <p>Graph of 2 lines in quadrant 1. Horizontal axis, time in weeks, scale 0 to 12, by 1’s. Vertical axis, amount saved in dollars, scale 0 to 100, by 20’s. Lin line, y intercept = 10. Slope = 20. Jada line, y intercept = 20, slope= 10.</p>

The value where a line intersects the vertical axis is called the vertical intercept . When the vertical axis is labeled with a variable like \(y\) , this value is also often called the \(y\) -intercept . Jada's graph has a vertical intercept of \$20 while Lin's graph has a vertical intercept of \$10. These values reflect the amount of money they each started with. At 1 week they will have saved the same amount, \$30. But after week 1, Lin is saving more money per week (so she has a larger rate of change), so she will end up saving more money over the summer if they each follow their plans.

Glossary Entries

A linear relationship between two quantities means they are related like this: When one quantity changes by a certain amount, the other quantity always changes by a set amount. In a linear relationship, one quantity has a constant rate of change with respect to the other.

The relationship is called linear because its graph is a line.

The graph shows a relationship between number of days and number of pages read.

When the number of days increases by 2, the number of pages read always increases by 60. The rate of change is constant, 30 pages per day, so the relationship is linear.

The vertical intercept is the point where the graph of a line crosses the vertical axis.

The vertical intercept of this line is \((0,\text-6)\) or just -6.

A graph of a line with a vertical intercept of -6

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Be prepared for the 2023 – 2024 academic year by doing summer course work early! In these documents, you will find access to the course work, as well as the respective faculty member teaching the class. If there are any questions, please email the faculty members in charge of their class.

AP Students

LHS AP Agreement Form 2023-2024

Please use the link below to access the English department's Summer Reading List for 2024. 

English Department Summer Reading List 2024

AP Language Summer Reading Assignment 2024

URI WRT104 Summer Reading Assignment 2024 - TBA

AP English Literature Summer Reading Assignment 2024

College Planning

College Search/Information

SAT/ACT dates

Apply To College via Common Application

College Financial Aid Information

All Math Courses can find their summer work here  

Fundamentals of Math Summer Assignment 2023

Computer Science JavaScript Google Classroom Code: TBA

AP Computer Science Principles Google Classroom Code: TBA

AP Computer Science A Google Classroom Code: TBA

AP Physics 1 – Access via Mr. Garriott’s Google Classroom, code: x4lnngl 

AP Biology – Access via Mr. Souness’ Google Classroom, code: TBA

Social Studies

AP US Government and Politics click here for summer work PDF and Access via Mr. Almeida's Google Classroom, code: 6ero7xi

AP World History: click here for summer work PDF and Access via Mrs. Lane’s Google Classroom, code: p7lr4sv  

AP US History ( click here for work ) – Access via Mr. Allen's Google Classroom, code: 3cn34x3  

AP Human Geography - Access via Mrs. Carr's Google Classroom code: TBA

AP Psychology Summer Assignment 2023: TBA

Unified Arts

AP Studio Art Summer Work 2023

All State Audition pieces

Students are encouraged to use the digital practice files provided, or to work with their private instructors to prepare for November 2022 audition date. Requirements are found below:

  • Band – Junior All State (9th Graders only)
  • Band – Senior All State (10th, 11th, 12th grade only)
  • Chorus – Junior All State (9th graders only)
  • Chorus – Senior All State (10th, 11th, 12th grade only)

VHS Learning

All AP VHS homework can be found here or Login to the VHS portal via email sent from your class

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COMMENTS

  1. Illustrative Mathematics

    6.3: Summer Reading. Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days. After day 1, Lin reaches page 70, which matches the point she made on her graph.

  2. Grade 8 Mathematics, Unit 3.6

    6.3 Summer Reading. Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days. After day 1, Lin reaches page 70, which matches the point she made on her graph.

  3. Lin has a summer reading assignment. After reading the first 30 pages

    Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days. After day 1, Lin reaches page 70, which matches the point (1,70) She made it on her graph.

  4. Illustrative Mathematics Grade 8, Unit 3.6

    Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days. After day 1, Lin reaches page 70, which matches the point \((1,70)\) she made on her graph.

  5. 3.2.2: More Linear Relationships

    Exercise \(\PageIndex{3}\): Summer Reading. Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. ... Jada's graph has a vertical intercept of $20 while Lin's graph has a vertical intercept of $10. These values reflect the amount of money they each started with.

  6. More Linear Relationships

    Lesson 6.3 Summer Reading. Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days. After day 1, Lin reaches page 70, which matches the point (1,70) she made on her ...

  7. Summer Reading Assignments: How to Make Them Fun and Engaging

    Fold the paper in half three times hamburger style, return to the first fold, cut in the center on the folded side up to the crease, return to an unfolded sheet, fold the paper hotdog style, push the two ends together, and fold it into a book shape. Whichever you choose, model the book-folding process for students.

  8. Tips for Creating Summer Reading Assessment Ideas (Plus 3 Fun Ideas!)

    Character Awards. To freshen up your summer reading assignment, try having students create unique and interesting awards for the characters. This is a good way for students to recall information and analyze character development at the same time. Ask students to come up with the award and the reason why that character earned it.

  9. PDF Middle School (Entering grades 6-8) Summer Reading List

    ENTERING 7TH GRADE SUMMER READING ASSIGNMENT. Students will Where the Mountain Meets the Moon Grace Lin. by Students will produce a written response ... • Create a vertical line down the middle of the page • Label the left column TEXT and the right column RESPONSE 3. Divide your novel into five (5) equal sections. ...

  10. Summer Reading in AP Lit.

    THE OLD SUMMER READING ASSIGNMENT. My summer assignment has gone through different iterations over the years, but the gist of it has always been that the students had to read two books — How to Read Literature Like a Professor: A Lively and Entertaining Guide to Reading Between the Lines and 1984 — and develop an outline for each. There are ...

  11. Summer Reading

    The goal of summer reading is to develop the habit and love of reading. Finding a quiet time 4-5 times a week for reading will support young learners in maintaining and growing skills important in the first grade. If your child cannot yet read independently, reading with your child is just as important to develop a habit of reading.

  12. PDF The AP Language and Composition

    A Rationale: Summer Reading—Why? Why? Why? Dear Student, Believe us, we know that reading for English class and the tedious writing involved with SUMMER READING is not your number one priority this summer. Rather, it's likely you are looking forward to long, languid days at the beach and a myriad of Netflix sessions on the couch. (Wait?

  13. Summer Reading

    Summer Reading. NEST+m is a community of readers. Each summer, our students receive grade-specific reading assignments. Please see the information below for Lower, Middle and Upper Grades summer reading assignments. All books have been carefully chosen by our ELA teachers. Before starting your assignment, please read the important information ...

  14. PDF 2021-2022 AP Language and Composition: Summer Reading Assignments

    The more detailed your work, the more support you'll have for the in-class essay the first week of school. To learn more about the general guidelines regarding summer reading as well as the required assignments for each text , please read below. I look forward to working with you this year! Assignment #1 : Walden by Henry David Thoreau

  15. Lin has a summer reading assignment. After reading the first 30 pages

    Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days. After day 1, Lin reaches page 70, which matches the point (1,70) she made on her graph.

  16. PDF 9th-Grade Summer Reading Assignment

    9th-Grade Summer Reading Assignment. Dear Incoming Freshman, Welcome to Pali High! As your future English teachers, we have a small request: pick a book that you are excited to read this summer. This book is your choice, but please make sure you choose a book that you've never read before.

  17. About Summer Assignments

    Summer History. All incoming middle school students (grades 6-8) have summer HISTORY assignments, in addition to summer reading assignments. Students should be prepared for a review of the material and tests at the beginning of the school year. Please click on your campus link to the left to review the assignments for your campus middle school ...

  18. PDF Summer Reading/Activity List for AP Literature and Composition*

    How to Read Literature Like a Professor by Thomas C. Foster (ISBN: 978--0623-0167-3) Assignment for Book #1: Create a digital notebook in a Google doc. (If you do not have access to a computer this summer, you can create a handwritten notebook.) At the very beginning, type out a schedule with your own deadlines to complete the reading of all ...

  19. Illustrative Mathematics

    Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days. After day 1, Lin reaches page 70, which matches the point \((1,70)\) she made on her graph.

  20. PDF AP Literature & Composition 2016 Summer Reading Assignments

    Summer '16 Assignments include two novels, one assignedand one independentchoice: Assigned novel: East of Edenby John Steinbeck We will discuss this novel when we return to school in August. I would suggest reading this novel second—that way, it will be fresh in your mind, facilitating a more lively class conversation.

  21. PDF The AP Literature and Composition

    expect to see specific line-by-line edits and constructive feedback where appropriate. In some cases, a more detailed rubric will be issued for projects and presentations due to the grading differentiation of such summative assessments. Below, please study the checklists as you complete your summer assignments. Meeting these minimum checklist

  22. Summer Assignments / Summer Assignments

    Please use the link below to access the English department's Summer Reading List for 2023. Students entering each grade have a choice between two books; students should select one of the books to read over the summer. There is an opportunity for bonus points on the summer reading assessment, which has 25 reading comprehension questions.

  23. PDF ENC 1101/1102 Summer Reading Assignment 2020-2021

    ENC 1101/1102 Summer Reading Assignment 2020-2021 . ... Assignment Directions: For your Summer Reading Assignment you are required you to read Stephen King's On Writing: A Memoir of the Craft. As you read you are required to respond to the questions provided in complete and thoughtful sentences, making sure to use quotes from the book ...