Question

For two months, Martin used the same snow removal company to help clear his property. The company had a fixedreservation rate per month plus an hourly rate for the amount of time that is spent clearing snow. Martin receivedtwo bills from the snow removal company. The first bill was $170 for 3 hours of snow removal and the second billwas $220 for 5 hours of snow removal. Find the equation of the line that represents the snow removal company'sfixed reservation rate and charge per hour. Round to the nearest cent if necessary.

Answer 1

The form of the equation of the line is

$y=mx+b$

where m is the slope and b is the y-intercept

In this case we will use

$170 for 3 hours as a point (3,170)

$220 for 5 hours as a pint (5,220)

First, we will use the next formula to find the slope of the line

$m=\frac{y_2-y_1}{x_2-x_1}$

In this case

(3,170)=(x1,y1)

(5,220)=(x2,y2)

we substitute

$m=\frac{220-170}{5-3}=\frac{50}{2}=25$

Then we calculate the the y-intercept using one point

$170=25(3)+b$$b=170-75=95$

The equation is

$y=25x+95$