Answer
$$y = -x + 5$$
Work Step by Step
If the line in question has the same y-intercept as the line $2y = 6x + 8$, then if we transform this equation into the slope-intercept form, then we will have the y-intercept of the line we are looking for.
If we divide both sides by $2$, then we have isolated $y$ to one side of the equation, and we also have the slope-intercept form of the equation:
$$y = \frac{6}{2}x + \frac{8}{2}$$
Divide to simplify:
$$y = 3x + 4$$
We see that the y-intercept for this line is $4$; therefore, the y-intercept of the line we are looking for is also $4$.
The line that we are looking for is parallel to the line with equation $4x + 4y = 20$. If the lines are parallel, that means that they also share the same slope. Let's put this equation into the slope-intercept form as well to find the slope of this equation:
We want $y$ on one side of the equation, so we want, first of all, to subtract $4x$ from each side of the equation:
$$4y = -4x + 20$$
Now, to solve for $y$, we divide both sides by $4$:
$$y = -x + 5$$
The slope of this line is $-1$, which means the line we are interested in also has a slope of $-1$.
Now that we have the slope and y-intercept, we can set up the equation for the line that we are looking for:
$$y = -x + 5$$
