Question

How do you find the slope that is perpendicular to the line `3x-5y=-8`?

Answer 1

See a 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

`color(red)(3)x - color(blue)(5)y = color(green)(-8)`

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

Substituting and calculating `m` gives:

`m = color(red)(-3)/color(blue)(-5) = 3/5`

Let's call the slope of the perpendicular line: `m_p`

The formula to find the slope of a perpendicular line is:

`m_p = -1/m`

Substituting the slope we calculated above gives:

`m_p = -1/(3/5)`

`m_p = -5/3`