Answer:
third option
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 = - 2x - 5 ← is in slope- intercept form
with slope m = - 2
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}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (- 1, 1) into the partial equation
1 = - [tex]\frac{1}{2}[/tex] + c ⇒ c = 1 + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{3}{2}[/tex] ← equation of perpendicular line
