How do you write the equation in point slope form given (1,2) and (-1,-4)?

Jul 28, 2016

$y - 2 = 3 \left(x - 1\right)$
or
$y + 4 = 3 \left(x + 1\right)$

Explanation:

The slope of a line between $\left(1 , 2\right)$ and $\left(- 1 , - 4\right)$ is
$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{m} = \frac{\Delta y}{\Delta x} = \frac{2 - \left(- 4\right)}{1 - \left(- 1\right)} = \frac{6}{2} \textcolor{g r e e n}{= 3}$

The general form of a slope-point equation is
$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{b l u e}{b} = \textcolor{g r e e n}{m} \left(x - \textcolor{red}{a}\right)$
for a line with slope $\textcolor{g r e e n}{m}$ through a point $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$

We could use either $\left(\textcolor{red}{1} , \textcolor{b l u e}{2}\right)$ or $\left(\textcolor{red}{- 1} , \textcolor{b l u e}{- 4}\right)$ for our point $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$

Using $\left(\textcolor{red}{1} , \textcolor{b l u e}{2}\right)$ the slope-point equation would be:
$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{b l u e}{2} = \textcolor{g r e e n}{3} \left(x - \textcolor{red}{1}\right)$