Answer
The slope of the line perpendicular to the one given is $\frac{5}{2}$.
Work Step by Step
We know that perpendicular lines have slopes that are negative reciprocals of one another.
Let's go ahead and find the slope of the equation given first. We want to convert this equation to the slope-intercept form so that we can easily locate the slope of this line. The slope-intercept form is given by the formula:
$y = mx + b$
where $m$ is the slope and $b$ is the $y$-value of the $y$-intercept.
Let's solve this equation for $y$.
Subtract $2x$ from both sides of the equation to isolate the $y$ term on the left side:
$5y = -2x + 10$
Divide both sides of the equation by $5$ to solve for $y$:
$y = -\frac{2}{5}x + \frac{10}{5}$
Let's simplify the equation by simplifying the fraction:
$y = -\frac{2}{5}x + 2$
The slope of this line is, therefore, $-\frac{2}{5}$.
The slope of the line perpendicular to this one must be the negative reciprocal of this slope.
We figure the negative reciprocal by flipping this fraction upside-down and reversing its sign.
Therefore, the slope we are looking for is:
$m = \frac{5}{2}$
