Question

what is the point slop equation of the line through the points (-5,5) that is perpendicular to the line whose equation is 5x=3y​

Answer 1

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

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Given

5x = 3y , that is

3y = 5x ( divide both sides by 3 )

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

with slope m =
`(5)/(3)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((5)/(3) )` = -
`(3)/(5)` and (a, b) = (- 5, 5), then

y - 5 = -
`(3)/(5)` (x - (- 5) ), that is

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

Answer 2

(2, -10)

Explanation:

5-3= 2

-5-5= -10