Question

How do you find the slope that is perpendicular to the line `2x+3y=7`?

Answer 1

`3/2`

Explanation:

Rearrange the equation into the form y=mx+c where m is the gradient and c is the y intercept.

`y=-2/3x+7`

The slope that is perpendicular to that line has a gradient with the negative reciprocal i.e. change the sign from minus to plus (or vice versa) and then flip it upside down.

`-2/3` becomes `3/2`

You need a little more information to find the resulting equation i.e. a point which the line goes through where you will reuse the equation above (y=mx+c) to find the new y intercept.

Answer 2

See a solution process below:

Explanation:

This equation is in Standard Linear 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

`color(red)(2)x + color(blue)(3)y = color(green)(7)`

The slope of an equation in standard form is: `m = -color(red)(2)/color(blue)(3)`

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

The formula for this slope is the inverse negative of the slope of the other line, or:

`m_p = -1/m`

Therefore:

`m_p = -1/(-2/3) = 3/2`