Answer:
Please check the explanation.
Step-by-step explanation:
Given the table
Minutes 6 15 27
Pages 20 50 90
Given two points to find the slope
Finding the slope between (6, 20) and (15, 50)
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [50 - 20] / [15 - 6]
= 30 / 9
= 10/3
Thus, the slope = m = 10/3
Using the point-slope form of the linear line function
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 10/3 and the point (6, 20)
[tex]y-20=\frac{10}{3}\left(x-6\right)[/tex]
Add 20 to both sides
[tex]y-20+20=\frac{10}{3}\left(x-6\right)+20[/tex]
[tex]y=\frac{10}{3}x-20+20[/tex]
[tex]y=\frac{10}{3}x[/tex]
Therefore, the rule relating the minutes, x, to the number of pages, y.
[tex]y=\frac{10}{3}x[/tex]
Determining the number of pages when the minutes equal 72
We already got the equation or rule relating the minutes, x, to the number of pages, y.
[tex]y=\frac{10}{3}x[/tex]
substitute x = 72
[tex]y=\frac{10}{3}\left(72\right)[/tex]
[tex]y=\frac{720}{3}[/tex]
[tex]y=240[/tex]
Therefore, the total pages are 240 when the minutes equal 72
