Respuesta :
Answer:
y = [tex]\frac{1}{3}[/tex] x - 8
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 )
rearrange 3x + y = - 5 into this form
subtract 3x from both sides
y = - 3x - 5 ← in slope-intercept form
with slope m = - 3
given a line with slope m then the slope of a lin e perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex], hence
[tex]m_{perpendicular}[/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, - 7 ) into the partial equation
- 7 = 1 + c ⇒ c = - 7 - 1 = - 8
y = [tex]\frac{1}{3}[/tex] x - 8 ← equation of perpendicular line
