# How do you find a standard form equation for the line with (6, -1) and is perpendicular to the line whose equation is 5x + 9y - 61 = 0?

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Nam D. Share
Dec 31, 2017

$y = \frac{9}{5} x - \frac{59}{5}$

#### Explanation:

First, convert $5 x + 9 y - 61 = 0$ into $y = m x + b$

$5 x + 9 y - 61 = 0$

Therefore, $y = - \frac{5}{9} x + \frac{61}{9}$

The perpendicular line to $y = - \frac{5}{9} x + \frac{61}{9}$ will have a slope $m = \frac{9}{5}$, because the product of the perpendicular line's slope and the original line's slope (${m}_{1} {m}_{2}$) will equal $- 1$.

${y}_{2} = \frac{9}{5} x + c$ where $c$ is the y-intercept

We know that it passes through $\left(6 , - 1\right)$. Plug that in to ${y}_{2}$.

$- 1 = \frac{54}{5} + c$

$c = - \frac{59}{5}$

Therefore, the equation of the line that passes through $\left(6 , - 1\right)$ and is perpendicular to $5 x + 9 y - 61 = 0$ is

$y = \frac{9}{5} x - \frac{59}{5}$

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