# How do you find slope of the line perpendicular to the line 5x+2y=10?

Apr 19, 2018

$\text{perpendicular slope } = \frac{2}{5}$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{rearrange "5x+2y=10" into this form}$

$\text{subtract 5x from both sides and divide all terms by 2}$

$2 y = - 5 x + 10$

$\Rightarrow y = - \frac{5}{2} x + 5 \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{with slope } = - \frac{5}{2}$

$\text{given a line with slope m then the slope of a line}$
$\text{perpendicular to it is}$

•color(white)(x)m_(color(red)"perpendicular")=-1/m

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{- \frac{5}{2}} = \frac{2}{5}$

Apr 19, 2018

The way we find the equations for a family of perpendicular lines is to swap the coefficients on $x$ and $y$ and negate one of them: $2 x - 5 y = \textrm{c o n s \tan t}$ or $y = \frac{2}{5} x + \textrm{c o n s \tan t}$, a slope of $\frac{2}{5}$.