Answer:
[tex](a)\ y = -0.75x + 26[/tex]
[tex](b)\ y = 14.75[/tex]
Step-by-step explanation:
Given
See attachment for scatter plot
Required
Equation of the line of best fit
Pick any two points on the line
[tex](x_1,y_1) = (24,8)[/tex]
[tex](x_2,y_2) = (8,20)[/tex]
Calculate the slope (m)
[tex]m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
[tex]m =\frac{20-8}{8-24}[/tex]
[tex]m =\frac{12}{-16}[/tex]
[tex]m =-0.75[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = -0.75(x - 24) + 8[/tex]
[tex]y = -0.75x + 18 + 8[/tex]
[tex]y = -0.75x + 26[/tex]
Solving (b): y, when [tex]x = 15[/tex]
[tex]y = -0.75x + 26[/tex] becomes
[tex]y = -0.75*15 + 26[/tex]
[tex]y = -11.25 + 26[/tex]
[tex]y = 14.75[/tex]
