Answer:
y = 5x + 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 )
y = - [tex]\frac{1}{5}[/tex] x + 9 is in this form
with slope m = - [tex]\frac{1}{5}[/tex]
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], hence
[tex]m_{perpendicular}[/tex] = - 1 / - [tex]\frac{1}{5}[/tex] = 5
y = 5x + c ← is the partial equation
to find c substitute (- 2, - 2) into the partial equation
- 2 = - 10 + c ⇒ c = - 2 + 10 = 8
y = 5x + 8 ← equation of perpendicular line
