Question

Find the slope of a line perpendicular to the line whose equation is 5x-4y=-24. Fully simplify your answer.

Answer 1

Answer: -4/5

Explanation:

Answer 2

m = -4/5

Explanation:

We can find the slope of the line perpendicular to 5x - 4y = -24 using the formula

`m_(2)=-(1)/(m_(1) )`

where m2 is the slope of the line we don't know and m1 is the slope of the line we're given.

Currently, 5x - 4y = -24 (Ax + By = C) and we convert it to slope intercept form (y = mx + b), where m is the slope and thus our m1 value:

`(5x-4y=-24)-5x\\(-4y=-5x-24)/-4\\y=(-5)/(-4)x+(-24)/(-4)\\ y=5/4x+6`

Since 5/4 is our m1 value, we simply plug it into the first equation above to find the slope of the other line (aka our m2 value):

`m_(2)=-(1)/((5/4))\\ m_(2)=-4/5`