Answer:
y = 3x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 4) and (x₂, y₂ ) = (3, 2) ← 2 points on the line
m = [tex]\frac{2-4}{3+3}[/tex] = [tex]\frac{-2}{6}[/tex] = - [tex]\frac{1}{3}[/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{1}{3} }[/tex] = 3, thus
y = 3x + c ← is the partial equation
To find c substitute (- 1, 4) into the partial equation
4 = - 3 + c ⇒ c = 4 + 3 = 7
y = 3x + 7 ← equation of perpendicular line
