# How do you write the equation of a line that passes through (-4, 3) and (2, 6)?

Jun 7, 2017

See below.

#### Explanation:

We first need to find the slope of the line.

slope$= \frac{6 - 3}{2 - \left(- 4\right)} = \frac{3}{6} = \frac{1}{2}$

We know that the equation of a line takes on the form $y = m x + b$, where $m$ is the slope and $b$ is the $y$-intercept.

Thus, we can plug in our answer to get:

$y = \frac{1}{2} x + b$

However, we know a point $\left(x , y\right)$ on this line-- $\left(2 , 6\right)$. We can plug this in as well.

$6 = \frac{1}{2} \left(2\right) + b$

$6 = 1 + b$

$b = 5$.

So, our final equation is:

$y = \frac{1}{2} x + 5$