Answer:
[tex]y -8= \frac{9}{2}(x +6)[/tex]
Step-by-step explanation:
Given
[tex]f(-6) = 8[/tex]
[tex]f(-8) = -2[/tex]
Required
Determine the equation in point-slope form
The general function notation is:
[tex]f(x) = y[/tex]
So, in [tex]f(-6) = 8[/tex]
[tex](x_1,y_1) = (-6,8)[/tex]
[tex]f(-8) = -1[/tex]
[tex](x_2,y_2) = (-8,-1)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2-x_1}[/tex]
[tex]m = \frac{-1-8}{-8-(-6)}[/tex]
[tex]m = \frac{-1-8}{-8+6}[/tex]
[tex]m = \frac{-9}{-2}[/tex]
[tex]m = \frac{9}{2}[/tex]
The equation is then calculated as:
[tex]y -y_1= m(x-x_1)[/tex]
[tex]y -8= \frac{9}{2}(x - (-6))[/tex]
[tex]y -8= \frac{9}{2}(x +6)[/tex]
