Answer:
y = - 3x + 11
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 )
y = [tex]\frac{1}{3}[/tex] x - 3 ← is in slope- intercept form
with slope m = [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, then
y = - 3x + c ← is the partial equation
To find c substitute (3, 2) into the partial equation
2 = - 9 + c ⇒ c = 2 + 9 = 11
y = - 3x + 11 ← equation of perpendicular line
