Q55. - Algebra 2

Question

What is the slope of a line perpendicular to a line with slope $-\frac{\mathbf{1}}{\mathbf{2}}$?

  (A) -2            (B) $-\frac{\mathbf{1}}{\mathbf{2}}$                      (C) $\frac{\mathbf{1}}{\mathbf{2}}$                        (D) 2

Step-by-Step Solution

Answer

The slope of a line perpendicular to a line with slope $-\frac{1}{2}$ is 2. So, (D) is the correct option.

Step 1 – State the formula

The slope of a line perpendicular to a line having slope m is $-\frac{1}{m}$.

Step 2 – List the given data

The slope of a line is $-\frac{1}{2}$. The objective is to find the slope of a line perpendicular to this line.

Step 3 – Calculate the slope

Put $m=-\frac{1}{2}$ in $-\frac{1}{m}$ to get,

$\begin{array}{c}-\frac{1}{m}=-\frac{1}{-\frac{1}{2}}\\ =\frac{1}{\frac{1}{2}}\\ =2\end{array}$

So, the slope of the line perpendicular to this line is 2.