Answer:
y = [tex]\frac{1}{3}[/tex] x + 4
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 this 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]
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (3, 5 ) into the partial equation
5 = 1 + c ⇒ c = 5 - 1 = 4
y = [tex]\frac{1}{3}[/tex] x + 4 ← equation of perpendicular line
