Question

Some carpet cleaning costs are shown in the table. The relationship is linear. Find and interpret the rate of change

Answer 1

y = m x + b , where m is the slope. The slope is the rise over the run or the change in x ( rooms cleaned ) over the change in y ( cost ).

125 = m * 1 + b

175 = m * 2 + b

-----------------------

b = 125 - m

175 = 2 m + 125 - m

m = 175 - 125

m = 50 ( the rate of change ), b = 75

The formula is: y = 50 x + 75

It means that the starting cost will be $75 and that for every room cleaned, the cost will rise for $50.

Answer 2

y = m x + b , where m is the slope. The slope is the rise over the run or the change in x ( rooms cleaned ) over the change in y ( cost ).
125 = m * 1 + b
175 = m * 2 + b
-----------------------
b = 125 - m
175 = 2 m + 125 - m
m = 175 - 125
m = 50 ( the rate of change ), b = 75
The formula is: y = 50 x + 75
It means that the starting cost will be $75 and that for every room cleaned, the cost will rise for $50.