# Question #7356c

Dec 11, 2017

$- \frac{1}{5} x - \frac{6}{5} = y$

#### Explanation:

First, remember that the equation $- \frac{1}{m} x + b = y$ is perpendicular to $m x + b = y$

First, write $5 x - y = 3$ in the intercept form $y = m x + b$

$5 x - y = 3$
$5 x = 3 + y$
$5 x - 3 = y$

Since the slope is 5, the slope for the perpendicular line is $- \frac{1}{5}$

Since this line perpendicular to $5 x - 3 = y$ passes through (4,-2), we can use the formula $m \left(x - {x}_{1}\right) = y - {y}_{1}$ to find the equation.

$- \frac{1}{5} \left(x - 4\right) = y - \left(- 2\right)$ We need to make this into the form $y = m x + b$

$- \frac{1}{5} \left(x - 4\right) = y - \left(- 2\right)$

$- \frac{x}{5} + \frac{4}{5} = y + 2$
$- \frac{x}{5} + \frac{4}{5} - 2 = y$
$- \frac{x}{5} - \frac{6}{5} = y$
$- \frac{1}{5} x - \frac{6}{5} = y$
That is our answer! To prove this, simply graph these two points. Dec 11, 2017

$y + 2 = - \setminus \frac{1}{5} \left(x - 4\right)$

#### Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other.

So the perpendicular line will have a slope of $- \setminus \frac{1}{5}$.

Now we can write the equation in point-slope form:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$\setminus \implies y + 2 = - \setminus \frac{1}{5} \left(x - 4\right)$