Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points. $(-1,-2)$ and $(0,0)$
(a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope of the line that is parallel is $m=$
B. The slope of the line that is parallel is undefined.
(b) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope of the line that is perpendicular is $m=$
B. The slope of the line that is perpendicular is undefined.
Next

Step 1 ：First, we need to find the slope of the line passing through the points $(-1,-2)$ and $(0,0)$. The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Step 2 ：Then, we know that the slope of a line parallel to a given line is equal to the slope of the given line. So, the slope of the line parallel to the line passing through the points $(-1,-2)$ and $(0,0)$ is the same as the slope of this line.

Step 3 ：Finally, the slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. So, the slope of the line perpendicular to the line passing through the points $(-1,-2)$ and $(0,0)$ is the negative reciprocal of the slope of this line.

Step 4 ：Calculate the slope of the line passing through the points $(-1,-2)$ and $(0,0)$, we get $m = 2.0$

Step 5 ：The slope of the line that is parallel to the line passing through the points $(-1,-2)$ and $(0,0)$ is $m_{parallel} = 2.0$

Step 6 ：The slope of the line that is perpendicular to the line passing through the points $(-1,-2)$ and $(0,0)$ is $m_{perpendicular} = -0.5$

Step 7 ：Final Answer: (a) The slope of the line that is parallel is $m=\boxed{2.0}$ (b) The slope of the line that is perpendicular is $m=\boxed{-0.5}$