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.
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.
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.
Solution
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(From Unit 5, Lesson 9.)