The equation of a line in the slope-intercept form is:
[tex]y=mx+b[/tex]
By comparison with the given line:
[tex]y=3x[/tex]
We can see that m is 3. This value is the slope of the line.
A line perpendicular to it will have a slope:
[tex]\begin{gathered} m^{\prime}=-\frac{1}{m} \\ m^{\prime}=-\frac{1}{3} \end{gathered}[/tex]
Thus, the slope of a line perpendicular to y = 3x is:
[tex]-\frac{1}{3}[/tex]
