Question

How do you find the slope that is perpendicular to the line `y=(-3x)`?

Answer 1

Slope of the perpendicular: `color(green)(1/3)`

Explanation:

The standard general form of a linear equation in slope-intercept form is:
`color(white)("XXX")y=color(green)(m)x+color(blue)(b)`
with slope `color(green)(m)` and y-intercept `color(blue)(b)`.

The given equation `y=(-3x)`
can be re-written to be in explicit slope-intercept form as:
`color(white)("XXX")y=color(green)(""(-3))x+color(blue)(0)`
with slope `color(green)(""(-3))`

If a line has a slope of `color(m)`
then all lines perpendicular to it have a slope of `color(green)(""(-1/m))`

Since `y=-3x` has a slope of `color(green)(m=-3)`
any line perpendicular to it will have a slope of
`color(white)("XXX")color(green)((-1/m)=-(1/(-3))=1/3`