Answer:
[tex]y = -2x +7[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-3,13)[/tex]
[tex](x_2,y_2) = (6,-5)[/tex]
Required
Determine the equation in slope intercept form
First, we calculate the slope:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
The equation becomes:
[tex]m = \frac{-5 - 13}{6 - (-3)}[/tex]
[tex]m = \frac{-5 - 13}{6 +3}[/tex]
[tex]m = \frac{-18}{9}[/tex]
[tex]m = -2[/tex]
The equation is then calculated using:
[tex]y -y_1 = m(x - x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - 13 = -2(x -(-3))[/tex]
[tex]y - 13 = -2(x +3)[/tex]
[tex]y - 13 = -2x -6[/tex]
Make y the subject
[tex]y = -2x - 6 + 13[/tex]
[tex]y = -2x +7[/tex]
