# How do you write the equation of the line between the points (2, 4) and (-2,8)?

##### 2 Answers
Jan 7, 2017

See full process description below:

#### Explanation:

We can use the point-slope formula to write this equation.

However, first we must find the slope.

The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the two points from the problem gives:

$m = \frac{\textcolor{red}{8} - \textcolor{b l u e}{4}}{\textcolor{red}{- 2} - \textcolor{b l u e}{2}}$

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

$m = - 1$

Now we can use the point slope formula.

The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the slope we calculate and one of the points gives:

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- 1} \left(x - \textcolor{red}{2}\right)$

Putting this in the more familiar slope-intercept form by solving for $y$ gives:

$y - \textcolor{red}{4} = \textcolor{b l u e}{- 1} x - \left(\textcolor{b l u e}{- 1} \times \textcolor{red}{2}\right)$

$y - \textcolor{red}{4} = \textcolor{b l u e}{- 1} x - \left(- 2\right)$

$y - \textcolor{red}{4} = \textcolor{b l u e}{- 1} x + 2$

$y - \textcolor{red}{4} + 4 = \textcolor{b l u e}{- 1} x + 2 + 4$

$y - 0 = \textcolor{b l u e}{- 1} x + 6$

$y = - x + 6$

Jan 7, 2017

$x + y - 6 = 0$

#### Explanation:

You can find the line by the following formula:

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

where (x_1;y_1) and (x_2;y_2) are the given points.

Then the line is:

$\frac{y - 4}{8 - 4} = \frac{x - 2}{- 2 - 2}$

$\frac{y - 4}{4} = \frac{x - 2}{-} 4$

$y - 4 = - x + 2$

$x + y - 6 = 0$