Answer:
• y=0.03x+50
,• $185
Explanation:
The slope-intercept form of the equation of a line is:
[tex]y=mx+b,m=\text{slope,b}=y-\text{intercept}[/tex]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.
[tex]\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{146-125}{3200-2500} \\ =\frac{21}{700} \\ m=0.03 \end{gathered}[/tex]Next, substitute the value of m.
[tex]\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}[/tex]The slope-intercept form representing the total cost, y, to clean a house with x square feet is:
[tex]y=0.03x+50[/tex](b) When the house is 4500 square feet.
[tex]\begin{gathered} y=0.03(4500)+50 \\ =135+50 \\ =\$185 \end{gathered}[/tex]