# How do you find a standard form equation for the line with (-1, 5), parallel to x + y = 10?

Jun 6, 2017

$y = - x$

#### Explanation:

We need a line parallel to $y = 10 - x$ passing through $\left(- 1 , 5\right)$. Parallel lines have the same gradient, so our required line will have a gradient of $- 1$.

Now we need to use the formula to find the equation of a line given two points and the gradients:

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

$y - 5 = - \left(x + 5\right)$

$y - 5 = - x - 5$

$y = - x$