Answer:
y = - 4x + 15
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{x}{4}[/tex] - 2 ← is in slope- intercept form
with slope m = [tex]\frac{1}{4}[/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] = - [tex]\frac{1}{\frac{1}{4} }[/tex] = - 4 , then
y = - 4x + c ← is the partial equation
to find c, substitute (4, - 1 ) into the partial equation
- 1 = - 16 + c ⇒ c = - 1 + 16 = 15
y = - 4x + 15 ← equation of perpendicular line
