# What is the equation of the line perpendicular to y=-5/11x  that passes through  (1,-3) ?

Dec 7, 2015

$11 x - 5 y = 26$

#### Explanation:

$y = - \frac{5}{11} x$ has a slope of $\left(- \frac{5}{11}\right)$

For any line with a slope of $m$ all lines perpendicular to it have a slope of $\left(- \frac{1}{m}\right)$

Therefore any line perpendicular to $y = - \frac{5}{11} x$ has a slope of $\frac{11}{5}$.

If such a line passes through the point $\left(1 , - 3\right)$ then we can write its equation in the slope-point form ($y - \hat{y} = m \left(x - \hat{x}\right)$)

So our required line can be written as:
$\textcolor{w h i t e}{\text{XXX}} y - \left(- 3\right) = \frac{11}{5} \left(x - 1\right)$

While this is a valid answer to the given question, we would normally simplify it and convert it into standard form:

$\textcolor{w h i t e}{\text{XXX}} 5 \left(y + 3\right) = 11 \left(x - 1\right)$

$\textcolor{w h i t e}{\text{XXX}} 5 y + 15 = 11 x - 11$

$\textcolor{w h i t e}{\text{XXX}} 26 = 11 x - 5 y$

$\textcolor{w h i t e}{\text{XXX}} 11 x - 5 y = 26$