Find the slope of the line and write the slope as a rate of change. Don't forget to attach the proper units.
-The graph shows the total cost y (in dollars)of owning and operating a mini-van where x is the number of miles driven.
A)$0.43 per mile
B)cannot be determined
C)$2.33 per mile
D)$20.00 per mile

Question

Find the slope of the line and write the slope as a rate of change. Don't forget to attach the proper units.
-The graph shows the total cost y (in dollars)of owning and operating a mini-van where x is the number of miles driven.  
A)$0.43 per mile 
B)cannot be determined 
C)$2.33 per mile 
D)$20.00 per mile

Quizplus · Accepted Answer

To find the slope, we need to choose two points on the line and calculate the change in y over the change in x. One point that is easy to read is (100, $48) and another is (200, $91). The change in y is 91-48=$43 and the change in x is 200-100=100. The slope (rate of change) is therefore 43/100=0.43 dollars per mile. Choice A is the closest answer to this calculation. To find the slope of the line, we need to calculate the rise/run or change in y/change in x. Looking at the graph, we can see that for every 50 miles driven, there is a corresponding increase in cost of $21.50. So, the rate of change or slope is (change in y/change in x) = $21.50/50 miles = $0.43/mile. Thus, the answer is A.

Find the Slope of the Line and Write the Slope