Answer:
y = [tex]\frac{4}{3}[/tex] x - 12
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{3}{4}[/tex] x ← is in slope- intercept form
with slope m = - [tex]\frac{3}{4}[/tex] , c = 0
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{3}{4} }[/tex] = [tex]\frac{4}{3}[/tex] , then
y = [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute (3, - 8) into the partial equation
- 8 = 4 + c ⇒ c = - 8 - 4 = - 12
y = [tex]\frac{4}{3}[/tex] x - 12 ← equation of perpendicular line
