Answer:
y = - [tex]\frac{1}{3}[/tex] x
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 - 19 ← in slope- intercept 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] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute (6, - 2 ) into the partial equation
- 2 = - 2 + c ⇒ c = - 2 + 2 = 0
y = - [tex]\frac{1}{3}[/tex] x ← equation of perpendicular line
