Question

Hi! please help! give a full clear answer pls! thank you!

Answer 1

Answer: y =
`(3)/(2)`x + 7

Explanation:

First, we will write the given equation in slope-intercept form. To do this we will isolate the y-variable.

2x + 3y = 21 ➜ y = -
`(2)/(3)`x + 7

A perpendicular line will have the negative reciprocal as it's slope. Then, we will substitute the given coordinate point to solve for the y-intercept.

y = mx + b

y =
`(3)/(2)`x + b

4 =
`(3)/(2)`(-2) + b

4 = -
`(6)/(2)` + b

4 = -3 + b

7 = b

Lastly, we can create our equation.

y = mx + b

y =
`(3)/(2)`x + 7