Equations of Straight Line

For a straight line $\ell$ with slope $m$ and passing through a point $(x_1,y_1)$, the equation of $\ell$ is
$$y-y_1=m(x-x_1).$$

For a straight line $\ell$ passing through two points $(x_1,y_1)$ and $(x_2,y_2)$, the equation of $\ell$ is
$$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}.$$

For a straight line $\ell$ with slope $m$ and $y$ intercept $c$, the equation of $\ell$ is
$$y=mx+c.$$

For a straight line $\ell$ with $x$ intercept $a$ and $y$ intercept $b$, the equation of $\ell$ is
$$\frac{x}{a}+\frac{y}{b}=1.$$

For any straight line $\ell$, the equation of $\ell$ can be rewritten to the form
$$Ax+By+C=0,$$
where $A$, $B$ and $C$ are integers.

1. Slope $={\displaystyle \frac{-A}{B}}$
2. $y$ intercept $={\displaystyle \frac{-C}{B}}$
3. $x$ intercept $={\displaystyle \frac{-C}{A}}$