Model real-world situations with linear relationships.
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In this lesson, students bring several concepts and skills together to be able to model and interpret real-world linear situations. The Problem Set Guidance includes several resources that can be used in connection to this lesson or as part of a review for the unit.
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 or 2 (benefit from discussion) . Find more guidance on adapting our math curriculum for remote learning here.
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A student has had a collection of baseball cards for several years. Suppose that B, the number of cards in the collection, can be described as a function of $$t$$, which is time in years since the collection was started.
Explain what each of the following equations would tell us about the number of cards in the collection over time.
Baseball Cards, accessed on Dec. 6, 2016, 3:22 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
You have $100 to spend on a barbeque where you want to serve chicken and steak. Chicken costs $1.30 per pound and steak costs $3.50 per pound. You want to know how many pounds of chicken and steak you can afford to buy.
Chicken and Steak, Variation 1, accessed on Feb. 26, 2018, 11:31 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Modified by Fishtank Learning, Inc.?
The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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A parking garage is located in the downtown area of a city. The table below shows the cost for parking in the garage for different amounts of time.
Hours Parked | Cost of Parking |
1 | $8.80 |
$$1 \frac{1}{2}$$ | $10.70 |
4 | $20.20 |
5 | $24 |
$$7 \frac{1}{2}$$ | $33.50 |
10 | $43 |
a. What equation represents the cost of parking in the garage, $$y$$, for $$x$$ hours?
b. Sketch a graph to represent the cost of parking over time.
c. What does the slope of your line represent in context of this situation?
d. What does the $$y$$-intercept of your line represent in context of this situation?