Question

How do you find the slope that is perpendicular to the line `y=1/3x+6`?

Answer 1

Slope: `color(red)(-3)`

Explanation:

If a line has a slope of `color(green)(m)`
then any line perpendicular to it has a slope of `color(red)(-1/m)`

Equations in the form:
`color(white)("XXX")y=color(green)(m)x+color(blue)(b)`
are in "slope-intercept form" with a slope of `color(green)(m)`

The given equation:
`color(white)("XXX")y=color(green)(1/3)x+color(blue)(6)`
is in this "slope-intercept form" with a slope of `color(green)(1/3)`

Any line perpendicular to it has a slope of
`color(white)("XXX")color(red)(-1/(""(1/3))=-3`