Question

3. ** Adrienne is a hairstylist at a new salon. She pays a monthly fee to rent a station at the salon. The graph below represents the profit she makes each month based on the number of haircuts she performs.

Answer 1

In the graph is represented Adrienne's profit/month (y-axis) based on the number of haircuts she made (x-axis)

a. To determine her profit when she does 21 haircuts, you have to identify the number in the x-axis, go up until you reach the lines, and then left following the horizontal line to see the corresponding value of y (profit)

When she makes 21 haircuts, the makes a profit of $150

b.

To determine the line you need to use the following formula

`m=(y_1-y_2)/(x_1-x_2)`

Where

m is the slope

(x₁,y₁) are the coordinates of one point of the line

(x₂,y₂) are the coordinates of a second point of the line

You have to use two points of the line, for example, (12,0) and (15,50), replace them in the formula:

`\begin{gathered} m=(50-0)/(15-12) \\ m=(50)/(3) \\ m\cong16.67 \end{gathered}`

The slope of the line is $16.67/haircut

c.

The slope represents the variation in y for every unit increase of x.

In the context of the story, the slope indicates that Adrienne's profit increases by $16.67 for every increase of one haircut she performs.