# How do you find the slope and intercept of x-y=1?

Jul 28, 2018

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: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

The $y$-intercept of an equation in standard form is: $\frac{\textcolor{g r e e n}{C}}{\textcolor{b l u e}{B}}$

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

Therefore:

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

• The $y$-intercept is: $\frac{\textcolor{g r e e n}{1}}{\textcolor{b l u e}{- 1}} = - 1$ or $\left(0 , - 1\right)$

$1 ,$ & x-intercept is $1$ & y-intercept is $- 1$

#### Explanation:

Given equation of straight line is

$x - y = 1$

$\frac{x}{1} + \frac{y}{-} 1 = 1$

The above equation is in standard intercept form of line: $\frac{x}{a} + \frac{y}{b} = 1$ which has

x-intercept: $a = 1$

y-intercept: $b = - 1$

The given equation of line:

$x - y = 1$

$y = x - 1$

The above equation is in standard slope-intercept form: $y = m x + c$ with slope

$m = 1$

Slope: $m = 1$

Jul 30, 2018

Slope: $1$, $y$-intercept $- 1$

#### Explanation:

Recall slope-intercept form

$y = m x + b$, with slope $m$ and a $y$-intercept of $b$.

We essentially just want a $y$ on the left side. Let's subtract $x$ from both sides to get

$- y = - x + 1$

Next, divide both sides by $- 1$ to get

$y = x - 1$

Now, our equation is in slope-intercept form, with a slope of $1$, and a $y$-intercept of $- 1$.

Hope this helps!