# What is the slope and intercept of x-y=6?

Jul 25, 2017

See a solution process below:

#### Explanation:

This equation is in Standard Linear form. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

$x - y = 6$ is:

$\textcolor{red}{1} x + \textcolor{b l u e}{- 1} y = \textcolor{g r e e n}{6}$

Therefore the slope is: $m = \frac{\textcolor{red}{- 1}}{\textcolor{b l u e}{- 1}} = 1$

To find the $y$ intercept, set $x$ to $0$ and solve for $y$:

$x - y = 6$ becomes:

$0 - y = 6$

$- y = 6$

$\textcolor{red}{- 1} \cdot - y = \textcolor{red}{- 1} \cdot 6$

$y = - 6$

Therefore, the $y$-intercept is: $- 6$ or $\left(0 , - 6\right)$

If you also need the $x$ intercept, do the opposite. Set $y$ to $0$ and solve the $x$:

$x - y = 6$ becomes:

$x - 0 = 6$

$x = 6$

Therefore, the $x$-intercept is: $6$ or $\left(6 , 0\right)$