A transportation company will carry specialty deliveries for a distance of 800 miles. The cost for the first 500 miles is $0.90 per mile and then $2.50 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 $0.90 per mile for the first 500 miles. This means that for each added mile, the price increases at a constant rate of $0.90. Because the increase is constant with each mile, the graph should be linear before 500 miles with a slope of 0.90. 
After 500 miles, the rate increases to $2.50 per mile. This means the slope of the line will increase and become steeper. For each mile added after 500 miles, $2.50 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 500 with a bend at 500. The line after 500 will have a steeper slope than the line before. The only graph that satisfies these requirements is the one above.

A Transportation Company Will Carry Specialty Deliveries for a Distance