# What is the equation of the line perpendicular to y=-11/16x  that passes through  (3,7) ?

May 20, 2018

$16 x - 11 y = - 29$

#### Explanation:

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

•color(white)(x)y=mx+b

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

$y = - \frac{11}{16} x \text{ is in this form with } m = - \frac{11}{16} , b = 0$

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

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

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{- \frac{11}{16}} = \frac{16}{11}$

$\Rightarrow y = \frac{16}{11} + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(3,7)" into the partial equation}$

$7 = \frac{48}{11} + b \Rightarrow b = \frac{77}{11} - \frac{48}{11} = \frac{29}{11}$

$\Rightarrow y = \frac{16}{11} x + \frac{29}{11} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$\text{multiply all terms by 11 and rearrange}$

$11 y = 16 x + 29$

$\Rightarrow 16 x - 11 y = - 29 \leftarrow \textcolor{red}{\text{in standard form}}$