Lesson 8

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slopes don’t have to be positive

Warm Up

Lesson

Summary

Cool

Down

Reflections

Student

Task

Learning

Targets

Practice Problems

Lesson Video

Unit 5

linear relationships

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8.1 Warm Up - which one doesn’t belong: odd line out

Which line doesn’t belong?

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Learning Targets

• In this lesson, students get their first glimpse of lines that visually slope downhill as well as a “flat” line or line with 0 slope.

• 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.

Success Criteria

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8.2 stand clear of the closing doors, please

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8.2 stand clear of the closing doors, please

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

a. 0 rides? b. 1 ride? c. 2 rides? d. x rides?

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

3. 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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8.3 travel habits in july

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

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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Are you Ready for more?

Let’s say you have taken out a loan and are paying it back. Which of the following graphs have positive slope and which have negative slope?

1. Amount paid on the vertical axis and time since payments started on the horizontal axis.
2. Amount owed on the vertical axis and time remaining until the loan is paid off on the horizontal axis.
3. Amount paid on the vertical axis and time remaining until the loan is paid off on the horizontal axis.

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8.4 payback plan

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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lesson synthesis

How would you figure out the slope of these lines?

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Lesson Summary

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Lesson Summary

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Lesson Summary

The vertical intercept is 5, since the graph starts when she has $5 on her fare card. The slope of the graph is since she doesn’t use her fare card for the next year, meaning the amount on her fare card doesn’t change for a year. In fact, all graphs of linear relationships with slopes equal to 0 are horizontal—a rate of change of 0 means that, from one point to the next, the y-values remain the same.

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8.5 Cool Down: the slopes of graphs

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

1. Calculate the slope of graph D. Explain or show your reasoning.

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2. Calculate the slope of graph E. What situation could the graph represent?

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3. On the blank grid, draw a line that passes through the indicated point and has slope -2

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Reflections

• Can you give an example of a situation that would have a negative slope when graphed?

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• Can you look at a graph and tell if the slope is positive or negative and explain how you know?

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Practice Problems

Must do: All problems

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Lesson Video

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