Question

A cleaning company charged $125 to clean a 2500 square foot house. The same company charged $146 to clean a 3200 square foot house. Write an equation in slope-intercept form to represent the total cost, y, to clean a house with x square feet. Then. find the total cost to clean a house that is 4500 square feet.this is confusing me so badly I'm getting a headache step by step explanation and solving might help me thank you.

Answer 1

• y=0.03x+50

,

• $185

Step-by-step explanation:

The slope-intercept form of the equation of a line is:

`y=mx+b,m=\text{slope,b}=y-\text{intercept}`

The number of square feet = x

The cost of cleaning x square feet = y

From the given information:

• When x=2500 square foot, y=$125; and

,

• When x=3200 square foot, y=$146

First, we find the slope of the line.

`\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =(146-125)/(3200-2500) \\ =(21)/(700) \\ m=0.03 \end{gathered}`

Next, substitute the value of m.

`\begin{gathered} y=0.03x+b \\ At\text{ (2500,125)} \\ 125=0.03(2500)+b \\ b=125-0.03(2500) \\ b=125-75 \\ b=50 \end{gathered}`

The slope-intercept form representing the total cost, y, to clean a house with x square feet is:

`y=0.03x+50`

(b) When the house is 4500 square feet.

`\begin{gathered} y=0.03(4500)+50 \\ =135+50 \\ =\$185 \end{gathered}`