Answer:
y = [tex]\frac{1}{3}[/tex] x + [tex]\frac{20}{3}[/tex]
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 + 2 ← 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 (4, 8) into the partial equation
8 = [tex]\frac{4}{3}[/tex] + c ⇒ c = 8 - [tex]\frac{4}{3}[/tex] = [tex]\frac{20}{3}[/tex]
y = [tex]\frac{1}{3}[/tex] x + [tex]\frac{20}{3}[/tex] ← equation of line
