# How do you find a standard form equation for the line with (4,-3) and is parallel to the line 2x+3y-6=0?

Jul 28, 2016

$y = - \frac{2}{3} x - \frac{1}{3}$

#### Explanation:

Lines which are parallel have the same slope.
Find the equation of the given line by changing it into standard form. $y = m x + c$

$2 x + 3 y - 6 = 0 \text{ } \Rightarrow 3 y = - 2 x + 6$

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

We also have a point on the line, $\left(4 , - 3\right)$

Use the formula: $y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - \left(- 3\right) = - \frac{2}{3} \left(x - 4\right)$

$y + 3 = - \frac{2}{3} x + \frac{8}{3}$

$y = - \frac{2}{3} x + \frac{8}{3} - 3 \text{ } 2 \frac{2}{3} - 3$

$y = - \frac{2}{3} x - \frac{1}{3}$