Question

How do you find the slope that is perpendicular to the line `5x + 2y = 6`?

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)`

Therefore the slope of `color(red)(5)x + color(blue)(2)y = color(green)(6)` is:

`m = -color(red)(5)/color(blue)(2)`

Let the slope of the perpendicular line be: `m_p`

The formula for the slope of a perpendicular line is:

`m_p = -1/m`

Substituting gives:

`m_p = (-1)/(-5/2) = 2/5`