# How do you write an equation of a line that contains (5, 7) and (-3, 11)?

Nov 8, 2016

$x + 2 y = 19$

#### Explanation:

The slope of a line through $\left(5 , 7\right)$ and $\left(- 3 , 11\right)$ is given by the relation:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{m} = \frac{\Delta y}{\Delta x} = \frac{11 - 7}{\left(- 3\right) - 5} = \textcolor{g r e e n}{- \frac{1}{2}}$

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

Using $\textcolor{g r e e n}{m = - \frac{1}{2}}$ as the slope and
$\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right) = \left(\textcolor{red}{5} , \textcolor{b l u e}{7}\right)$ as a point,
we have:
$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{b l u e}{7} = \textcolor{g r e e n}{- \frac{1}{2}} \left(x - \textcolor{red}{5}\right)$

While this could be considered a valid solution to the given question,
it is normal to convert this into standard form:

$\textcolor{w h i t e}{\text{XXX}} 2 y - 14 = - x + 5$

$\textcolor{w h i t e}{\text{XXX}} x + 2 y = 19$