First, we have to find the slope of the line. Let's use the points (30, 60) and (40, 80). Using the slope formula, we have.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let's replace the points.
[tex]m=\frac{80-60}{40-30}=\frac{20}{10}=2[/tex]
Then, we use one point, the slope, and the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-60=2(x-30) \\ y-60=2x-60 \\ y=2x-60+60 \\ y=2x \end{gathered}[/tex]
Then, we use this equation to find the items purchased for 80 seconds.
[tex]y=2\cdot80=160[/tex]
Therefore, if it takes 80 seconds to ring up a customer, the number of items purchased is 160.
