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 )
(a)
y = - 2x + 5 ← is in slope- intercept form
with slope m = - 2
Parallel lines have equal slopes , then
y = - 2x + c ← is the partial equation
To find c substitute (- 3, 2 ) into the partial equation
2 = 6 + c ⇒ c = 2 - 6 = - 4
y = - 2x - 4 ← equation of parallel line
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(b)
y = 3x + 4 ← 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] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute (3, 2 ) into the partial equation
2 = - 1 + c ⇒ c = 2 + 1 = 3
y = - [tex]\frac{1}{3}[/tex] x + 3 ← equation of perpendicular line
