# How do you find the slope that is perpendicular to the line 7x+2y=3?

Apr 8, 2018

color(brown)("Slope f the perpendicular line "color(indigo)(m_1 = -(1 / m) = 2/7

#### Explanation:

$7 x + 2 y = 3$

Standard form of slope intercept equation is $y = m x + c$ where m is the slope.

$2 y = - 7 x + 3$

$y = - \left(\frac{7}{2}\right) x + \frac{3}{2}$

Slope of the given line $m = - \left(\frac{7}{2}\right)$

Slope f the perpendicular line ${m}_{1} = - \left(\frac{1}{m}\right) = - \left(\frac{1}{- \frac{7}{2}}\right) = \frac{2}{7}$

Apr 8, 2018

$\text{perpendicular slope } = \frac{2}{7}$

#### Explanation:

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

•color(white)(x)y=mx+b

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

$\text{rearrange "7x+2y=3" into this form}$

$\text{subtract 7x from both sides}$

$\cancel{7 x} \cancel{- 7 x} + 2 y = - 7 x + 3$

$\Rightarrow 2 y = - 7 x + 3$

$\text{divide all terms by 2}$

$\Rightarrow y = - \frac{7}{2} x + \frac{3}{2} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$\text{with slope m } = - \frac{7}{2}$

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

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

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{- \frac{7}{2}} = \frac{2}{7}$