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 is. On a graph, their distances (in meters) from their homes is a function of the time (in seconds) from when they begin the race.

1. As you read the graphs left to right, would the lines go up or down?
2. What is different about the lines representing Kiran’s run and Clare’s run?
3. What is the same about the lines representing Kiran’s run and Clare’s run?

A car sharing service charges your account once a month according to how much you use their cars. The graph shows the amount charged for the month in dollars as a function of the number of miles driven.

1. Use this information to predict how many miles a customer would need to drive so that the monthly charge is $100.
2. Is the monthly charge a linear function of miles driven? Explain your reasoning.

Solve each of these equations. Explain or show your reasoning.