# What is the point-slope form of the line that passes through (-2,1) and (5,6)?

May 1, 2018

The point-slope formula is $y$$1$ =$m$$\left(x + 2\right)$, where $m$ is $\frac{5}{7}$.

#### Explanation:

$y$${y}_{1}$ =$m$(x−x_1)

$\left(- 2 , 1\right)$ = $\left({X}_{1} , {Y}_{1}\right)$
$\left(5 , 6\right)$ = $\left({X}_{2} , {Y}_{2}\right)$

$y$$1$ =$m$(x−-2)

Two negatives make a positive, so, this is your equation:

$y$ - $1$ = $m$$\left(x + 2\right)$

Here's how to solve for $m$ to plug-it into your point-slope formula:

$\frac{{Y}_{2} - {Y}_{1}}{{X}_{2} - {X}_{1}}$ = $m$, where $m$ is the slope.

Now, label your ordered pairs as ${X}_{1}$, ${X}_{2}$, ${Y}_{1}$, and ${Y}_{2}$:

$\left(- 2 , 1\right)$ = $\left({X}_{1} , {Y}_{1}\right)$
$\left(5 , 6\right)$ = $\left({X}_{2} , {Y}_{2}\right)$

Now, plug your data into the formula:

$\frac{6 - 1}{5 - - 2}$ = $m$

5 - - 2 becomes 5 + 2 because two negatives create a positive. Now, the equation is:

$\frac{6 - 1}{5 + 2}$ = $m$

Simplify.

$\frac{5}{7}$ = $m$

Therefore, $m$ = $\frac{5}{7}$.