Answer:
y = - 3x - 2
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 - [tex]\frac{2}{3}[/tex] ← 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 (1, - 5 ) into the partial equation
- 5 = - 3 + c ⇒ c = - 5 + 3 = - 2
y = - 3x - 2 ← equation of perpendicular line
