Question

What is the slope of a line perpendicular to `3x-7y =-2`?

Answer 1

See the complete answer explanation below:

Explanation:

This equation is in standard form. 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 = -A/B`

Therefore the slope of `color(red)(3)x - color(blue)(7)y = color(green)(-2)` can be found by substituting as follows:

`m = -3/-7 = 3/7`

The slope of a line perpendicular to the line in the problem (let's call it `m_p`) will have a slope which is the negative inverse or:

`m_p = -7/3`