# What is the equation of the line the passes through the points (6, 8) and (12, 4)?

Oct 31, 2015

$y = - \frac{2}{3} x + 12$

#### Explanation:

First step is to find the slope.

You do this by using the formula:

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

You can use the two points you are given. It doesn't mater which points you use first as long as the y goes on the top and the x on the bottom and keep the point together

$m = \frac{8 - 4}{6 - 12}$

$m = \frac{4}{- 6}$

$m = - \frac{2}{3}$

or

$m = \frac{4 - 8}{12 - 6}$

$m = \frac{- 4}{6}$

$m = - \frac{2}{3}$

Now that you have the slope you almost completed the equation

$y = - \frac{2}{3} x + b$

Use either points for x and y and solve for b

$8 = - \frac{2}{3} \left(6\right) + b$

$8 = - \frac{12}{3} + b$

$8 = - 4 + b$

$b = 12$

Plug b in

$y = - \frac{2}{3} x + 12$

Or

$4 = - \frac{2}{3} \left(12\right) + b$

$4 = - \frac{24}{3} + b$

$4 = - 8 + b$

$b = 12$

Plug b in

$y = - \frac{2}{3} x + 12$