# What is the line containing the points (0, 4) and (3, -2)?

Dec 14, 2016

$y - 4 = - 2 x$ or $y = - 2 x + 4$

#### Explanation:

To find the line containing these two points we must first determine the slope.

The slope can be found by using the formula: color(red)(m = (y_2 = y_1)/(x_2 - x_1)
Where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the two points.

Substituting our two points gives:

$m = \frac{- 2 - 4}{3 - 0}$

$m = \frac{- 6}{3}$

$m = - 2$

Next we can use the point-slope formula to find the equation for the line passing through the two points.

The point-slope formula states: $\textcolor{red}{\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)}$
Where $m$ is the slope and #(x_1, y_1) is a point the line passes through.

Substituting $- 2$ for $m$ and (0, 4) for the point gives:

$y - 4 = - 2 \left(x - 0\right)$

$y - 4 = - 2 x$

Now, solving for $y$ to put the equation in the slope-intercept format gives:

$y - 4 + 4 = - 2 x + 4$

$y - 0 = - 2 x + 4$

$y = - 2 x + 4$