Ryder Ferguson

2022-10-16

Find the equation of the line perpendicular to $y=\frac{9}{16}x$ that passes through (−1,5)

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yorbakid2477w6

Expert

A line perpendicular to $y=\frac{9}{16}x$ will have a slope of $-\frac{16}{9}$
So, with $m=-\frac{16}{9}\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}\left(-1,5\right)$ we can find the equation from:
$y-{y}_{1}=m\left(x-{x}_{1}\right)$
$y-5=-\frac{16}{9}\left(x-\left(-1\right)$
$y=-\frac{16}{9}x-\frac{16}{9}+5\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}-\frac{16}{9}=-1\frac{7}{9}$
$y=-\frac{16}{9}x+3\frac{2}{9}$

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