Answer:
y = - 2x + 5
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}{2}[/tex] x - 7 ← is 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 (4, - 3) into the partial equation
- 3 = - 8 + c ⇒ c = - 3 + 8 = 5
y = - 2x + 5 ← equation of perpendicular line
