Question

May I please receive help?

Answer 1

Parallel line,
`y=(3x)/(2) -(5)/(2)`

Perpendicular line,
`y=4-(2x)/(3)`

Explanation:

For the parallel line, In the equation y=mx+c, we are trying to find c.

We know that m=
`(3)/(2)`, so

we have the equation y=
`(3x)/(2) +c`

So we substitute the points we are given (3,2) into

`2=(3)/(2)*3+c\\Thus, c= (-5)/(2)`

The final equation we get is

`y=(3x)/(2) -(5)/(2)`

For the perpendicular line, we need to find the inverse of the slope.

The inverse of the slope
`(3)/(2) = -(2)/(3)`

So, we use this in our formula and also plug in the same coordinates we were given.

Therefore, we get:

`2= -(2)/(3)*3+a\\a=4\\\\y=4-(2x)/(3)`