Question

The total cost to mail a package to a different country is a function of the weight of the package in pounds. The table below shows the cost to mail packages of different weights.

Weight (pounds) Cost (dollars)
4 52
8 84
10 100
14 132
Which statement describes a graph which would represent the data in the table?

A.
a graph of an increasing nonlinear function with a y-intercept of 52 and a variable slope

B.
a graph of an increasing nonlinear function with a y-intercept of 20 and a variable slope

C.
a graph of an increasing linear function with a y-intercept of 8 and a slope of 20

D.
a graph of an increasing linear function with a y-intercept of 20 and a slope of 8

Answer 1

D.

The slopes between successive points are all (84−52)/(8−4)=32/4=8, (100−84)/(10−8)=16/2=8, (132−100)/(14−10)=32/4=8, so the data lie on a line with slope 8. Using y = 8x + b and (4,52) gives 52 = 32 + b, so b = 20. Hence an increasing linear function with y-intercept 20 and slope 8.