Question

Please help me out | Geometry

Answer 1

4th option

Explanation:

The equation of a line in slope- intercept form is

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

y =
`(7)/(5)` x - 3 ← is in slope- intercept form

with slope m =
`(7)/(5)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((7)/(5) )` = -
`(5)/(7)` , then

y = -
`(5)/(7)` x + c ← is the partial equation

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

4 =
`(20)/(7)` + c ⇒ c = 4 -
`(20)/(7)` =
`(28)/(7)` -
`(20)/(7)` =
`(8)/(7)`

y = -
`(5)/(7)` x +
`(8)/(7)` ← equation of perpendicular line