# What is the equation in point slope form that passes through the points (2, 1) and (-3, -6)?

May 10, 2018

$y - 1 = \frac{7}{5} \left(x - 2\right)$

or

$y + 6 = \frac{7}{5} \left(x + 3\right)$

#### Explanation:

Point slope form is written as $y - {y}_{1} = m \left(x - {x}_{1}\right)$

Use the slope formula with the two given points to find the slope of the line.

$m = \frac{1 - \left(- 6\right)}{2 - \left(- 3\right)} = \frac{7}{5}$

Now that we have our m, we can insert the x and y values of either point to create our line. We'll use (2, 1).

$y - 1 = \frac{7}{5} \left(x - 2\right)$

To check it, we can use the other point, (-3, -6)

$- 6 - 1 = \frac{7}{5} \left(- 3 - 2\right)$

$- 7 = \frac{7}{5} \cdot - 5$

$- 7 = - 7$

We can also say $y + 6 = \frac{7}{5} \left(x + 3\right)$ and check with (2,1)

$1 + 6 = \frac{7}{5} \left(2 + 3\right)$

$7 = 7$