# How do you find the slope and intercept of x-y=10?

May 8, 2018

Slope is $1$, $y$-intercept is $- 10$ and $x$-intercept is $10$.

#### Explanation:

Slope intercept form of equation of a line is

$y = m x + c$, where $m$ is its slope and $c$ is its intercept on $y$-axis

So if you want to know slope of a line and its intercept n $x$-axis, just express $y$ in terms of $x$ and coefficient of $x$ will be the slope and any constant term added to it will be its intercept on $y$ axis.

As we have $x - y = 10$, this means $x - y + y = 10 + y$

or $x = 10 + y$ i.e. $10 + y = x$ and hence

$10 + y - 10 = x - 10$

or $y = x - 10$ i.e. the form which we desired

Now as coefficient of $x$ is $1$, slope of line $1$

and as constant term is $- 10$, $y$-intercept is $- 10$

In case you want $x$ intercept, just put $y = 0$ in the equation

$x - y = 10$ and we get $x - 0 = 10$ or $x = 10$

Hence $x$-intercept is $10$

graph{x-10 [-20.33, 19.67, -14.8, 5.2]}