Answer:
C
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line
m = [tex]\frac{-4-2}{2-(-2)}[/tex] = [tex]\frac{-6}{2+2}[/tex] = - [tex]\frac{6}{4}[/tex] = - [tex]\frac{3}{2}[/tex]
and using (a, b ) = (2, - 4 ) , then
y - (- 4) = - [tex]\frac{3}{2}[/tex](x - 2) , that is
y + 4 = - [tex]\frac{3}{2}[/tex] (x - 2) → C
