# How do you write an equation in point slope form parallel to -2x-3y = -2 and passing through (2, -2)?

Feb 22, 2016

Since the lines are parallel, this means that their slope is equal.

#### Explanation:

$- 2 x - 3 y = - 2$

$- 3 y = - 2 + 2 x$

$y = \frac{2}{3} - \frac{2}{3} x$

The slope is $- \frac{2}{3}$

We can now use the point and the slope to the find the equation of the line by plugging our values into point slope form.

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

$y - \left(- 2\right) = - \frac{2}{3} \left(x - 2\right)$

$y + 2 = - \frac{2}{3} x + \frac{4}{3}$

$y = - \frac{2}{3} x - \frac{2}{3}$

Hopefully this helps!