Question

Write an equation of a line through the point (-5, -2)that is perpendicular to the x-axis. Also state the slope of the line. A. x = -5, m = 0B. y = -2, m = 0C. x = -5, m = undefinedD. y = -2, m = undefined

Answer 1

First let's take a look at the point (-5,-2) in the plane:

since we want an equation of a line that is perpendicular to the x-axis, it should look like this:

Therefore, the equation is x = -5. Now for the slope, we can easily see that the line passes through the points (-5,-2) and (-5,-3), so, if we calculate the slope we get something like this:

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}_{} \\ \Rightarrow m=\frac{-3.-(-2)}{-5-(-5)}=\frac{-3+2}{-5+5}=-\frac{1}{0} \end{gathered}$

which clearly is undefined.