# What is the equation of the line that contains the points with (x, y) coordinates (-3, 7) and (5, -1)?

Mar 15, 2018

$x + y = 4$

#### Explanation:

If $\left({x}_{1} , {y}_{1}\right) = \left(- 3 , 7\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(5 , - 1\right)$ are points on a straight line, then the slope of that line is
$\textcolor{w h i t e}{\text{XXX}} m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 1 - 7}{5 - \left(- 3\right)} = \frac{- 8}{8} = - 1$

Any general point $\left(x , y\right)$ on this line together with $\left({x}_{1} , {y}_{1}\right) = \left(- 3 , 7\right)$, for example must have this same slope"
$\textcolor{w h i t e}{\text{XXX}} \frac{y - {y}_{1}}{x - {x}_{1}} = - 1$
or
$\textcolor{w h i t e}{\text{XXX}} \frac{y - 7}{x - \left(- 3\right)} = - 1$

Simplifying further
$\textcolor{w h i t e}{\text{XXX}} y - 7 = \left(- 1\right) \cdot \left(x + 3\right)$

$\textcolor{w h i t e}{\text{XXX}} y - 7 = - x - 3$

In standard form:
$\textcolor{w h i t e}{\text{XXX}} x + y = 4$