# How do you find in standard form a line that is parallel to -2x-3y = -2 and passing through (2, -2)?

Mar 23, 2018

$- 2 x - 3 y = 2$

#### Explanation:

First, we need to find the slope of the line that it is parallel to, as this line will have the same slope.
$- 2 x - 3 y = - 2$
$3 y = - 2 x - 2$
$y = - \frac{2}{3} x - \frac{2}{3}$
Therefore, $m = - \frac{2}{3}$
We can use point-slope form at first before we convert it to standard form.
$y - {y}_{1} = m \left(x - {x}_{1}\right)$
$y + 2 = - \frac{2}{3} \left(x - 2\right)$
$y + 2 = - \frac{2}{3} x + \frac{4}{3}$
$3 y + 6 = - 2 x + 4$ multiply by 3 to get rid of fractions
$- 2 x - 3 y = 2$