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
\begin{equation*}
y-y_1 = m (x-x_1).
\end{equation*}

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

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

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

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

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