Answer:
[tex]y=-\frac{1}{3}x-5[/tex]
Step-by-step explanation:
We want to find the equation of the line passing through (3,-6), (-6, -3).
Write the formula for slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute [tex](x_1=3,y_1=-6),(x-2=-6,y_2=-3)[/tex]
[tex]m=\frac{-3--6}{-6-3}\\ m=\frac{3}{-9}\\m=-\frac{1}{3}[/tex]
Use the formula [tex]y=m(x-x_1)+y_1[/tex] to find the equation.
Substitute the point and slope to get:
[tex]y=-\frac{1}{3}(x-3)+-6[/tex]
Simplify:
[tex]y=-\frac{1}{3}x+1+-6[/tex]
[tex]y=-\frac{1}{3}x-5[/tex]
