Question

Determine the slope of the line that is perpendicular to the equation below.

y=-3x +4
Type your answer as a reduced fraction of necessary, like this 3/4

Answer 1

When the equation of a line is already in the form
`y = mx+q`, the slope is the coefficient of x, i.e. m.

So, in your case, the slope is -3.

Given a line with slope m, all perpendicular lines will have slope

`-\cfrac{1}{m}`

So, all lines perpendicular to a line with slope -3 have slope

`-\cfrac{1}{-3} = \cfrac{1}{3}`

Answer 2

Product of Slope of a line and its perpendicular is -1.

Suppose slope of a line is m1 and its perpendicular is m2.

`m1 * m2 = -1`

The general slope intercept form is given by :

`y=mx+b`

We are given the equation,

`y=-3x+4`

Comparing our equation with general slope intercept form , we have

slope (m1) = -3

slope of line perpendicular to it (m2) is given by formula above

`m1 * m2 = -1`

plugging m1=-3 in this

`(-3) * m2 = -1`

dividing both sides by -3,

m2 =1/3

So slope of line perpendicular to given line is 1/3.