# How do you write an equation of the line, in point-slope form, that passes through the two given points (-2,15), (9,-18)?

Apr 2, 2015

The answer is: $y - 15 = \left(- 3\right) \cdot \left(x + 2\right)$

The point slope form is:

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

$m$ is the slope of the line. So we should find the slope first. Slope is the amount of change in y-axis per the amount of change in x-axis.

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

When we plug our given points to this equation:

$m = \frac{15 - \left(- 18\right)}{- 2 - 9} \to \left(- 3\right)$

Now we found the slope of our line. We just need to plug one of the points to the point-slope equation. You can choose any of the given points. Since they are on the same line, final equations will be equivalent.

$y - 15 = \left(- 3\right) \cdot \left(x - \left(- 2\right)\right)$
$y - 15 = \left(- 3\right) \cdot \left(x + 2\right)$