# How do you write an equation of a line given (5, -2) parallel to line 3y+7x=-8?

Jul 7, 2017

$3 y + 7 x = 29$

#### Explanation:

Here's a quick trick: parallel lines in standard form will always have the same coefficients in front of the $x$ and $y$. So what we can do is write this equation:

3y + 7x = ?

This equation represents every possible line that is parallel to $3 y + 7 x = - 8$, and the value put in place of the question mark determines the placement of that line on the graph. So, to find the equation of the parallel line passing through $\left(5 , - 2\right)$, all we need to do is plug $\left(5 , - 2\right)$ into our equation and solve it.

$y = - 2$
$x = 5$

3y + 7x = ?

3(-2) + 7(5) = ?

-6 + 35 = ?

29 = ?

So we need to replace our ? with $29$.

$3 y + 7 x = 29$