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

May 27, 2017

$y = x - 6$

#### Explanation:

We can find the gradient of a perpendicular line by the negative inverse of the first line's gradient. So, as the gradient of the line you are given is -1, the gradient (m) of a line perpendicular to it would be $- \frac{1}{- 1}$ which is $- \left(- 1\right) = 1$

To find the equation of any line, we can use the formula
$y - {y}_{1} = m \left(x - {x}_{1}\right)$ where ${y}_{1}$ and ${x}_{1}$ are coordinates the line passes through.
Let's sub in our values - $m = 1$, ${x}_{1} = 5$ (from the coordinates) and ${y}_{1} = - 1$
So, $y - \left(- 1\right) = 1 \left(x - 5\right)$
$y + 1 = x - 5$
$y = x - 6$

Hope this helped; let me know if I can do anything else:)