Question

How do you find the slope that is perpendicular to the line `4x-3y = -24`?

Answer 1

See the solution process below:

Explanation:

This equation is in Standard Form for a linear equation. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

The slope of an equation in standard form is: `m = -color(red)(A)/color(blue)(B)`

Our equation is: `color(red)(4)x - color(blue)(3)y = color(green)(-24)`

Therefore the slope of the line in the equation is:

`m = (-color(red)(4))/color(blue)(-3) = 4/3`

Let's call the slope of a line perpendicular to the line in the problem:

`m_p`

The formula for a perpendicular line is:

`m_p = -1/m`

Substituting the slope we calculated for `m` gives:

`m_p = -1/(4/3) = -3/4`