A childcare center offers up to 60 hours of care for a child during the week. The center's policy is to charge $5 per hour for the first 8 hours of each day. After that, the center charges parents $2 an hour.
Which of the following graphs most accurately shows the relationship between the cost of child care and total hours?

Question

Quizplus · Accepted Answer

The price per hour starts at $5 per hour for the first 8 hours of each day. This means that for hours 1-8, the total price increases at a constant rate of $5.
Because the increase is constant with each hour, the graph should be linear before 8 hours with a slope of 5. 
After 8 hours, the rate decreases to $2 per hour. This means the slope of the line will decrease and become shallower. For each hour added after 8 hours, $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 8 with a bend at 8 The line after 8 will have a shallower slope than the line before. The only graph that satisfies these requirements is the one above.

A Childcare Center Offers Up to 60 Hours of Care