Question

George wants to hire someone to paint his new house. the graph below shows the cost, and dollars, based on the area painted, in square feet.

Answer 1

ANSWER

The cost increases $4 for every additional square foot being painted

OPTION A

Explanation:

To solve this particular problem, we need to find the slope/gradient of the line and the y-intercept on the y-axis.

To do this, we need to follow the steps below

Step 1: Pick any two points on the graph to calculate the slope

The points are (120, 480) and (360, 1440)

Let x1 = 120, y1 = 480, x2 = 360, y2 = 1440

`\begin{gathered} \text{Slope = }\frac{rise}{\text{run}} \\ \text{rise = y2 - y1} \\ \text{run = x2 - x1} \\ \text{Slope = }\frac{y2\text{ - y1}}{x2\text{ - x1}} \end{gathered}`

Substitute the above data into the slope formula

`\begin{gathered} \text{Slope = }\frac{1440\text{ - 480}}{360\text{ -120}} \\ \text{Slope = }(960)/(240) \\ \text{Slope = 4} \end{gathered}`

Hence, the slope of the line is 4

Step 2: Find the slope-intercept form

Recall, y = mx + b

Where m is the slope of the line

b is the intercept of the y-axis

`(y\text{ - y1) = m(x - x1)}`

m = 4, x1 = 120, and y1 = 480

Substitute the above data into the slope-intercept formula

Hence, the cost increases $4 for every additional square foot being painted