Answer:
y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Calculate the slope of line 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 ) = (0, - 3) ← 2 points on the line
m = [tex]\frac{-3-2}{0-(-2)}[/tex] = [tex]\frac{-5}{0+2}[/tex] = - [tex]\frac{5}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{5}{2} }[/tex] = [tex]\frac{2}{5}[/tex] , then
y = [tex]\frac{2}{5}[/tex] x + c ← is the partial equation in slope- intercept form
To find c substitute (3, 2 ) into the partial equation
2 = [tex]\frac{6}{5}[/tex] + c ⇒ c = 2 - [tex]\frac{6}{5}[/tex] = [tex]\frac{4}{5}[/tex]
y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{4}{5}[/tex] ← equation of perpendicular line
