Answer
$$y = -x + 2$$
Work Step by Step
If the line in question has the same y-intercept as the line $16y = 8x + 32$, 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 $16$, then we have isolated $y$ to one side of the equation, and we also have the slope-intercept form of the equation:
$$y = \frac{8}{16}x + \frac{32}{16}$$
Divide to simplify:
$$y = \frac{8}{16}x + 2$$
Simplify the fraction:
$$y = \frac{1}{2}x + 2$$
We see that the y-intercept for this line is $2$; therefore, the y-intercept of the line we are looking for is also $2$.
The line that we are looking for is parallel to the line with equation $3x + 3y = 9$. 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 $3x$ from each side of the equation:
$$3y = -3x + 9$$
Now, to solve for $y$, we divide both sides by $3$:
$$y = -x + 3$$
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:
$$y = -x + 2$$
