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 )
(1)
Given
y - 3 = - 2(x + 5) ← distribute parenthesis
y - 3 = - 2x - 10 ( add 3 to both sides )
y = - 2x - 7 ← in slope- intercept form
(2)
y = 3x + 5 ← is in slope- intercept form
with slope m = 3
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}{3}[/tex], thus
y = - [tex]\frac{1}{3}[/tex] + c ← is the partial equation
To find c substitute (3, - 2) into the partial equation
- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1
y = - [tex]\frac{1}{3}[/tex] x - 1 ← equation of line
