Question

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

Answer 1

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.

Answer 2

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

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