Answer:
y = - 2x
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
2y = x - 3 into this form
Divide all terms by 2
y = [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{1}{2}[/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}{2} }[/tex] = - 2, hence
y = - 2x + c ← is the partial equation of the perpendicular line
To find c substitute (- 1, 2) into the partial equation
2 = 2 + c ⇒ c = 2 - 2 = 0
y = - 2x ← equation of perpendicular line
