Answer
$$y = -2x - 4$$
Work Step by Step
We already know the y-intercept of this line. So the next piece is to find the slope of the equation.
We know from the information given that the line whose equation we are looking for is parallel to the line with equation $2x + y = 8$. In order for two lines to be parallel, they must have the same slope. If we can find the slope for this parallel line, then we know the slope for the line we are trying to find the equation for.
To find the slope of the parallel line, we want to isolate $y$ to put the equation into the slope-intercept form.
First, we subtract $2x$ from each side to get $y$ by itself:
$$y = -2x + 8$$
We have the line in slope-intercept form already, so we can examine the equation to find the slope.
From the formula for slope-intercept, $y = mx + b$, $m$ is the slope and the coefficient of the $x$ term. In this case, we have the slope as $-2$.
Now, let us put our y-intercept $-4$ and slope $-2$ into the slope-intercept form:
$$y = -2x - 4$$
