Answer:
y = - [tex]\frac{1}{3}[/tex] x + 1
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 = 3x + 5 is in this form with slope m = 3
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}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute (- 9, 4) into the partial equation
4 = 3 + c ⇒ c = 4 - 3 = 1
y = - [tex]\frac{1}{3}[/tex] x + 1 ← equation of perpendicular line
