Lesson 8
Linear Functions
Problem 1
Two cars drive on the same highway in the same direction. The graphs show the distance, \(d\), of each one as a function of time, \(t\). Which car drives faster? Explain how you know.
![Set of axes, horizontal, t, vertical d. Two lines labeled Car A and Car B both begin at the origin and climb as they go right, Car B climbs at a steeper angle.](https://staging-cms-im.s3.amazonaws.com/JWXWezTgbG3YXo9bUhjjbMrt?response-content-disposition=inline%3B%20filename%3D%228-8.5.C.PP.cars1.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.C.PP.cars1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T083623Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e6550ad1c67b3ad0d10c64904b359027016859043b845a2f777f3658d85b0956)
Solution
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Problem 2
Two car services offer to pick you up and take you to your destination. Service A charges 40 cents to pick you up and 30 cents for each mile of your trip. Service B charges $1.10 to pick you up and charges \(c\) cents for each mile of your trip.
- Match the services to the Lines \(\ell\) and \(m\).
- For Service B, is the additional
charge per mile greater or less than
30 cents per mile of the trip?
Explain your reasoning.
![Coordinate plane, horizontal, miles driven, 0 to 10, vertical, cost, dollars, 0 to 4. Line l through 0 comma 1 point 1, & 7 comma 2 point 5. Line m through 0 comma point 5, & 7 comma point 5.](https://staging-cms-im.s3.amazonaws.com/G1ZQSfLbNBWmS3xrj7KtyVM8?response-content-disposition=inline%3B%20filename%3D%228-8.5.C8.PP.Image.102.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.C8.PP.Image.102.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T083623Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b6498a83573032180575aa0db4a1fdceb7d984cbd2180e87bebf62c5e0d42afe)
Solution
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Problem 3
Kiran and Clare like to race each other home from school. They run at the same speed, but Kiran's house is slightly closer to school than Clare's house. On a graph, their distance from their homes in meters is a function of the time from when they begin the race in seconds.
- As you read the graphs left to right, would the lines go up or down?
- What is different about the lines representing Kiran's run and Clare's run?
- What is the same about the lines representing Kiran's run and Clare's run?
Solution
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Problem 4
Write an equation for each line.
![Five lines.](https://staging-cms-im.s3.amazonaws.com/HNfsbs5X5nZzYAahxKTj2fyB?response-content-disposition=inline%3B%20filename%3D%228-8.3.C11.PP.lines3.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.C11.PP.lines3.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T083623Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b532912343d8c89c65fa5ac760344cb407feeb834ca2cf355f655df2ff1f1daa)
Solution
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(From Unit 3, Lesson 11.)