In order to find the slope of a perpendicular line and of a parallel line, first let's identify the slope of the given line, comparing the equation with the slope-intercept model below:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Looking at the given line, we have m = -1/3.
The slope of a perpendicular line has the following relation with the slope of the line:
[tex]m_2=-\frac{1}{m_1}[/tex]Calculating the slope of the perpendicular line, we have:
[tex]m_2=-\frac{1}{-\frac{1}{3}}=\frac{1}{\frac{1}{3}}=3[/tex]Therefore the slope of a perpendicular line is m = 3.
The slope of a parallel line is the same as the slope of the given line, so the slope of a parallel line is m = -1/3.