Answer:
[tex]y=\frac{-1}{3}x-4[/tex]
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Define
Point (9, -7)
Point (-6, -2)
Step 2: Find slope m
[tex]m=\frac{-2-(-7)}{-6-9}[/tex]
[tex]m=\frac{-2+7}{-15}[/tex]
[tex]m=\frac{5}{-15}[/tex]
[tex]m=\frac{-1}{3}[/tex]
[tex]y=\frac{-1}{3}x+b[/tex]
Step 3: Find y-intercept b
[tex]-7=\frac{-1}{3}(9)+b[/tex]
[tex]-7=-3+b[/tex]
[tex]-4=b[/tex]
Step 4: Write linear equation in slope-intercept form
[tex]y=\frac{-1}{3}x-4[/tex]