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

##### 1 Answer

The perpendicular line's slope is

#### 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

**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

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