# How do you write the equation of the line that contains (-2, 5) and (4, 5)?

Nov 24, 2016

$y = 5$

#### Explanation:

First, find the slope of the line using this formula:

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

Where $m$ is the slope and

$\left(- 2 , 5\right) \implies \left({x}_{1} , {y}_{1}\right)$

$\left(4 , 5\right) \implies \left({x}_{2} , {y}_{2}\right)$

$m = \frac{5 - 5}{4 + 2} = \frac{0}{6} = 0$

Because the slope of this line is $0$, that means that the line is going to be a horizontal line.

Now, to find the equation of the line, use point slope form:

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

Choose a set of points to plug into ${x}_{1}$ and ${y}_{1}$

The equation should be the same regardless of the points you choose

Using $\left(- 2 , 5\right)$ and slope of $0$:

$y - 5 = 0 \left(x + 2\right)$

Distribute $0$ throughout the set of parenthesis

$y - 5 = 0 x + 0$

Perform the opposite operation to isolate y by adding $5$ on both sides of the equation

$y = 0 x + 5 \mathmr{and} y = 5$