Answer:
y = [tex]\frac{1}{3}[/tex] x - 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 = - 3x + 8 ← is 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] = [tex]\frac{1}{3}[/tex], thus
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute the coordinates of the x- intercept (6, 0) into the partial equation
0 = 2 + c ⇒ c = 0 - 2 = - 2
y = [tex]\frac{1}{3}[/tex] x - 2 ← equation of perpendicular line
