Answer:
see explanation
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 2x + y = - 5 into this form by subtracting 2x from both sides
y = - 2x - 5 ← 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], hence
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line
To find c substitute (- 1, - 2) into the partial equation
- 2 = - [tex]\frac{1}{2}[/tex] + c ⇒ c = - [tex]\frac{3}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex] ← equation in slope- intercept form
