# What is the equation of the line passing through (8,2), (5,8)?

Jan 4, 2016

In general form:

$2 x + y - 18 = 0$

#### Explanation:

The slope $m$ of a line passing through two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by the equation:

$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Let $\left({x}_{1} , {y}_{1}\right) = \left(8 , 2\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(5 , 8\right)$

Then:

$m = \frac{8 - 2}{5 - 8} = \frac{6}{- 3} = - 2$

The equation of the line passing through $\left(8 , 2\right)$ and $\left(5 , 8\right)$ can be written in point slope form as:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

That is:

$y - 2 = - 2 \left(x - 8\right)$

Add $2$ to both sides to find:

$y = - 2 x + 18$

which is the slope intercept form of the equation of the line.

Then putting all terms on one side by adding $2 x - 18$ to both sides we find:

$2 x + y - 18 = 0$

which is the general form of the equation of a line.