Answer:
y = 4x + 10
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}{4}[/tex] x + 3 ← 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, thus
y = 4x + c ← is the partial equation of the line
To find c substitute (- 3, - 2) into the partial equation
- 2 = - 12 + c ⇒ c = - 2 + 12 = 10
y = 4x + 10 ← equation of perpendicular line
