Answer
The slope of the line perpendicular to the given line is $\frac{1}{2}$.
Work Step by Step
With lines that are perpendicular to each other, the product of their slopes is $-1$; one slope is the negative reciprocal of the other. If we want to find the slope of a line that is perpendicular to a given line, we must first find the slope of the given line.
The line given is in the slope-intercept form, which is given by the formula:
$y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
Therefore, the slope of the given line is the coefficient of $x$, so the slope is $-2$.
Let us set up an equation to find the slope of the line that is perpendicular to the given line by multiplying the two slopes to yield $-1$. Let $x$ be the slope of the perpendicular line:
$(-2)(x) = -1$
Divide both sides by $-2$:
$x = \dfrac{1}{2}$
