Answer:
Parallel line, [tex]y=\frac{3x}{2} -\frac{5}{2}[/tex]
Perpendicular line, [tex]y=4-\frac{2x}{3}[/tex]
Step-by-step explanation:
For the parallel line, In the equation y=mx+c, we are trying to find c.
We know that m=[tex]\frac{3}{2}[/tex], so
we have the equation y=[tex]\frac{3x}{2} +c[/tex]
So we substitute the points we are given (3,2) into
[tex]2=\frac{3}{2}*3+c\\Thus, c= \frac{-5}{2}[/tex]
The final equation we get is
[tex]y=\frac{3x}{2} -\frac{5}{2}[/tex]
For the perpendicular line, we need to find the inverse of the slope.
The inverse of the slope [tex]\frac{3}{2} = -\frac{2}{3}[/tex]
So, we use this in our formula and also plug in the same coordinates we were given.
Therefore, we get:
[tex]2= -\frac{2}{3}*3+a\\a=4\\\\y=4-\frac{2x}{3}[/tex]
