Question

Paulina’s income from a job that pays her a fixed amount per hour is shown in the graph. use the graph to find how much income is earned for working 7 hours.

Answer 1

$\ 140$

1) We can note two things about Paulina's income, it is proportional to her working hours and it is modeled by a linear equation.

2) So, let's find the slope of the line picking two points along the line: (1,20) and (3,60) and plug them into the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{60-20}{3-1}=\frac{40}{2}=20$

Since the line passes through the origin (0,0) we can tell that b=0, and write:

$\begin{gathered} y=mx+b \\ y=20x+0 \\ y=20x \end{gathered}$

3) So, now we can find the income of Paulina if she works 7 hours plugging into x (hours):

$\begin{gathered} y=20(7) \\ y=140 \end{gathered}$