# Forms of Linear Equations

## Key Questions

• 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: $\frac{\textcolor{g r e e n}{C}}{\textcolor{b l u e}{B}}$

I have heard of four

#### Explanation:

Slope-intercept form: $y = m x + b$, where $m$ is the slope and $b$ is the y-intercept

Standard form: $a x + b y = c$

Point-slope form: $y - {y}_{1} = m \left(x - {x}_{1}\right)$, where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ is a point on the line

Intercept form: $\frac{x}{a} + \frac{y}{b} = 1$, where $a$ is the x-intercept and $b$ is the y-intercept