# How do you write an equation of a line passing through (3, -2), perpendicular to 11x-7y=9?

Oct 11, 2016

Please see the explanation for how it is done.

$y = - \frac{7}{11} x - \frac{1}{11}$

#### Explanation:

Begin by writing the given line in slope-intercept form so that you can obtain the slope, m, by observation:

$11 x - 7 y = 9$

$- \frac{11}{7} x + y = - \frac{9}{7}$

$y = \frac{11}{7} x - \frac{9}{7}$

The slope, m, of the given line is:

$m = \frac{11}{7}$

The slope, n, of all lines perpendicular to the given line is:

$n = - \frac{1}{m}$

$n = - \frac{1}{\frac{11}{7}}$

$n = - \frac{7}{11}$

The equation of all lines perpendicular is:

$y = - \frac{7}{11} x + b$

To find the desired line, we substitute the given point, $\left(3 , - 2\right)$ for x and y and then solve for b:

$- 2 = - \frac{7}{11} \left(3\right) + b$

$- \frac{22}{11} = - \frac{21}{11} + b$

$- \frac{22}{11} + \frac{21}{11} = b$

$b = - \frac{1}{11}$