Question

What is the slope of the line perpendicular to 3x+y=15?

Answer 1

The perpendicular line's slope is `1/3`.

Explanation:

Step 1: Convert the given line to slope-intercept form.

`color(white)(=>)3x+y=color(white)(–3x+)15`

`=>color(white)(3x+)y=–3x+15`

The slope of the given line is `–3`.

Step 2: Take the negative reciprocal of this slope.

`m=–3 " "=>" "m_"new"=–1/(–3)=1/3`

The slope of a line is a ratio of how far "up" the line goes relative to how far "right" it goes. If a line goes up by 3 every time it goes right 2, then the slope is `3/2.` This is commonly called "rise over run".

A perpendicular line is achieved by rotating the original line by 90°. Hence, the old rise of 3 becomes a new run of -3, and the old run of 2 becomes a new rise of 2. Meaning, the new slope will be `"new rise"/"new run" = 2/(–3)" "(=–2/3),` which is the negative reciprocal of the old slope.