Answer:
[tex]y = \frac{-x}{3} + 5[/tex]
Step-by-step explanation:
Given A (x₁, y₁) = ( -6, 7) and B (x₂, y₂) = (-3, 6)
Slope of line passing through points ( -6, 7) and (-3, 6) is:
m = [tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}} =\frac{6 - 7}{-3 + 6} =\frac{-1}{3}[/tex]
Now, the equation of line in point-slope form:
(y - y₁) = m (x - x₁)
Substituting the value of m and (x₁, y₁) = ( -6, 7) in above equation,
[tex](y - 7) = \frac{-1}{3}(x - (-6))[/tex]
[tex](y - 7) = \frac{-1}{3}(x + 6)[/tex]
[tex]3y - 21 = -x - 6[/tex]
[tex]3y = -x - 6 + 21[/tex]
[tex]3y = -x + 15[/tex]
[tex]y = \frac{-x + 15}{3}[/tex]
[tex]y = \frac{-x}{3} + 5[/tex]
Option B is the correct answer.
