Question

pls help fast!! Find the equation of a line perpendicular to 4x+3y=−24 that passes through the point (−8,3).

Answer 1

y - 3 =
`(3)/(4)` (x + 8)

Explanation:

the equation of a line in slope- intercept form is

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

given

4x + 3y = - 24 ( subtract 4x from both sides )

3y = - 4x - 24 ( divide through by 3 )

y = -
`(4)/(3)` x - 8 ← in slope- intercept form

with slope m = -
`(4)/(3)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(4)/(3) )` =
`(3)/(4)`

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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

here m =
`(3)/(4)` and (a, b ) = (- 8, 3 ) , then

y - 3 =
`(3)/(4)` (x - (- 8) ) , that is

y - 3 =
`(3)/(4)` (x + 8) ← equation of perpendicular line