Unit 3

Slopes Don't Have to be Positive

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Linear Relationships

Lesson 9

Expressions and Equations

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Let’s find out what a negative slope means.

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Unit 3 ● Lesson 9

Learning

Goal

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Which One Doesn’t Belong: Odd Line Out

Unit 3 ● Lesson 9 ● Activity 1

Which line doesn’t belong?

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Warm-up: Which One Doesn’t Belong?

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Stand Clear of the Closing Doors, Please

Unit 3 ● Lesson 9 ● Activity 2

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Stand Clear of the Closing Doors, Please

Unit 3 ● Lesson 9 ● Activity 2

Noah put $40 on his fare card. Every time he rides public transportation, $2.50 is subtracted from the amount available on his card.

1. How much money, in dollars, is available on his card after he takes
1. 0 rides?
2. 1 ride?
3. 2 rides?
4. x rides?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Stand Clear of the Closing Doors, Please

Unit 3 ● Lesson 9 ● Activity 2

2. Graph the relationship between amount of money on the card and number of rides.

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• How many rides can Noah take before the card runs out of money? Where do you see this number of rides on your graph?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Stand Clear of the Closing Doors, Please

Unit 3 ● Lesson 9 ● Activity 2

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Stand Clear of the Closing Doors, Please

Unit 3 ● Lesson 9 ● Activity 2

• Why does it make sense to say the slope of this graph is –2.5 rather than 2.5?
• If we let y represent the amount of money on the card, in dollars, and x the number of rides, the linear relationship in this activity has the equation y = 40 – 2.5x . When will there be no money left on the card?
• Does a point on the line such as (1.5, 36.25) makes sense in this situation?
• Which line has a slope of and which line has a slope of , and why.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Travel Habits in July

Unit 3 ● Lesson 9 ● Activity 3

What do you notice? What do you wonder?

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Notice and Wonder

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Travel Habits in July

Unit 3 ● Lesson 9 ● Activity 3

Here is a graph that shows the amount on Han’s fare card for every day of last July.

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1. Describe what happened with the amount on Han’s fare card in July.
2. Plot and label 3 different points on the line.
3. Write an equation that represents the amount on the card in July, y, after x days.
4. What value makes sense for the slope of the line that represents the amounts on Han’s fare card in July?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Travel Habits in July

Unit 3 ● Lesson 9 ● Activity 3

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Travel Habits in July

Unit 3 ● Lesson 9 ● Activity 3

What do you think the slope of the graph is, and why?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Payback Plan

Unit 3 ● Lesson 9 ● Activity 4

Elena borrowed some money from her brother. She pays him back by giving him the same amount every week. The graph shows how much she owes after each week.

Answer and explain your reasoning for each question.

1. What is the slope of the line?
2. Explain how you know whether the slope is positive or negative.
3. What does the slope represent in this situation?
4. How much did Elena borrow?
5. How much time will it take for Elena to pay back all the money she borrowed?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Slopes Don't Have to be Positive

Unit 3 ● Lesson 9

Pretend that your partner has been absent from class for a few days. Your job is to explain, verbally or in writing, how someone would figure out the slope of one of the graphed lines.

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Unit 3 ● Lesson 9

• I can give an example of a situation that would have a negative slope when graphed.
• I can look at a graph and tell if the slope is positive or negative and explain how I know.

Learning

Targets

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The Slopes of Graphs

Unit 3 ● Lesson 9 ● Activity 5

Each square on a grid represents 1 unit on each side.

1. Calculate the slope of graph D. Explain or show your reasoning.
2. Calculate the slope of graph E. What situation could the graph represent?
3. On the blank grid F, draw a line that passes through the indicated point and has slope -2.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

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