Answer
See the full explanation below.
Work Step by Step
(a)
Consider the equations of lines $y=\frac{1}{3}x+1$ and $y=-3x-2$.
If the equation of the line is of the form $y=mx+c$ -- that is, the slope intercept form -- then $m$ is called the slope of the line.
Therefore, the slope of the line $y=\frac{1}{3}x+1$ is $\frac{1}{3}$ and the slope of the line $y=-3x-2$ is $-3$.
Now, find the product of their slopes. If the product of their slope is $-1$, then the given two lines will be perpendicular.
${{m}_{1}}\cdot {{m}_{2}}=-1$
So, consider the product $\frac{1}{3}\times \left( -3 \right)=-1$
Hence, the given lines are perpendicular.
