Answer
$y = -\frac{1}{2}x - \frac{1}{2}$
Work Step by Step
1. The pattern equation for a line is:
$y = mx + b$
2. Firstly, we have to solve for y in $-2x -4y = 5$
$-2x = 5 + 4y $
$- 2 x - 5 = 4y$
$\frac{-2}{4}x - \frac{5}{4} = y$
$-\frac{1}{2}x - \frac{5}{4} = y$
- The "m" value for that equation is -$\frac{1}{2}$.
If two line equations are parallel, that means that they have the same slope, therefore, the same value for "m".
$y = -\frac{1}{2}x + b$
3. Now, we can use the given point $(-3,1)$ to solve for b:
$1 = -\frac{1}{2}(-3) + b$
$1 = \frac{3}{2} + b$
$1 - \frac{3}{2} = b$
$\frac{2}{2} - \frac{3}{2} = b$
$-\frac{1}{2} = b$
4. The equation of that line is:
$y = -\frac{1}{2}x - \frac{1}{2}$
