A recreation center offers transportation for summer campers with a maximum distance of 15 miles. The cost for the first 10 miles is $.75 per mile and then $2.00 per mile after that.
Which of the following graphs most accurately shows the relationship between the cost of transportation and total mileage?

Question

Quizplus · Accepted Answer

The price per mile starts at $0.75 per mile for the first 10 miles. This means that for each added mile, the price increases at a constant rate of $0.75. Because the increase is constant with each mile, the graph should be linear before 10 miles with a slope of 0.75. 
After 10 miles, the rate increases to $2 per mile. This means the slope of the line will increase and become steeper. For each mile added after 10 miles, $2 will be added to the total cost. The rate of increase is still constant, it is just increasing at a different constant rate. 
A graph that matches these conditions would be linear both before and after 10 with a bend at 10. The line after 10 will have a steeper slope than the line before. The only graph that satisfies these requirements is the one above.

A Recreation Center Offers Transportation for Summer Campers with a Maximum