When the equation of a line is already in the form [tex] y = mx+q [/tex], 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
[tex] -\cfrac{1}{m} [/tex]
So, all lines perpendicular to a line with slope -3 have slope
[tex] -\cfrac{1}{-3} = \cfrac{1}{3} [/tex]
Product of Slope of a line and its perpendicular is -1.
Suppose slope of a line is m1 and its perpendicular is m2.
[tex] m1 * m2 = -1 [/tex]
The general slope intercept form is given by :
[tex] y=mx+b [/tex]
We are given the equation,
[tex] y=-3x+4 [/tex]
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
[tex] m1 * m2 = -1 [/tex]
plugging m1=-3 in this
[tex] (-3) * m2 = -1 [/tex]
dividing both sides by -3,
m2 =1/3
So slope of line perpendicular to given line is 1/3.
