y = [tex]\frac{1}{3}[/tex] x + 2
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 3x + y = - 8 into this form
subtract 3x from both sides
y = - 3x - 8 ← in slope-intercept form
with slope m = - 3
given a line with slope m then the slope of a line perpendicular to it is
perpendicular slope = - [tex]\frac{1}{m}[/tex] = [tex]\frac{1}{3}[/tex]
y = [tex]\frac{1}{3}[/tex] x + c is the partial equation of the perpendicular
to find c substitute (- 3, 1 ) into the partial equation
1 = - 1 + c ⇒ c = 2
y = [tex]\frac{1}{3}[/tex] x + 2 ← in slope-intercept form
