Answer:
y = - 6x + 5
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}{6}[/tex] x + 3 ← is in slope- intercept form
with slope m = [tex]\frac{1}{6}[/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}{6} }[/tex] = - 6, hence
y = - 6x + c ← is the partial equation of the perpendicular line.
To find c substitute (- 3, 23) into the partial equation
23 = 18 + c ⇒ c = 23 - 18 = 5
y = - 6x + 5 ← equation of perpendicular line
