Question

Please help explanation if possible

Answer 1

y = -
`(3)/(2)` x + 1

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y =
`(2)/(3)` x +
`(2)/(3)` ← is in slope- intercept form

with slope m =
`(2)/(3)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((2)/(3) )` = -
`(3)/(2)` , then

y = -
`(3)/(2)` x + c ← is the partial equation

To find c substitute (- 2, 4) into the partial equation

4 = 3 + c ⇒ c = 4 - 3 = 1

y = -
`(3)/(2)` x + 1 ← equation of line