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 )
y = [tex]\frac{2}{3}[/tex] x - 6 ← is in slope- intercept form
with slope m = [tex]\frac{2}{3}[/tex]
Parallel lines have equal slopes , then
y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute (9, 2) into the partial equation
2 = 6 + c ⇒ c = 2 - 6 = - 4
y = [tex]\frac{2}{3}[/tex] x - 4 ← equation of parallel line
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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{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex] , then
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute (9, 2) into the partial equation
2 = - [tex]\frac{27}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{27}{2}[/tex] = [tex]\frac{31}{2}[/tex]
y = - [tex]\frac{3}{2}[/tex] x + [tex]\frac{31}{2}[/tex] ← equation of perpendicular line
