Answer:
y = - [tex]\frac{4}{3}[/tex] x - 7
Step-by-step explanation:
Parallel lines have equal slopes.
Calculate the slope m of the given line using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, - 2) ← 2 points on the line
m = [tex]\frac{-2-2}{3-0}[/tex] = - [tex]\frac{4}{3}[/tex], thus
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute P(- 3, - 3) into the partial equation
- 3 = 4 + c ⇒ c = - 3 - 4 = - 7
y = - [tex]\frac{4}{3}[/tex] x - 7 ← equation of parallel line
