Answer:
![y=\frac{1}{2}x+\frac{3}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B3%7D%7B2%7D)
Step-by-step explanation:
Let's write
to slope-intercept form.
We do this by solving for ![y](https://tex.z-dn.net/?f=y)
![-2x+4y=8\\](https://tex.z-dn.net/?f=-2x%2B4y%3D8%5C%5C)
Add 2x to both sides
![4y=8+2x](https://tex.z-dn.net/?f=4y%3D8%2B2x)
Divide both sides by 4
![y=\frac{1}{2} x+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7D%20x%2B2)
Now that we have that equation in slope-intercept form, the question wants us to find a line that is parallel to it that passes the point (-5, -1).
A line is parallel to another line is they have the same exact slope.
The slope is
.
Slope-intercept form:
, where
is the slope and
is the y-intercept.
So, let's see what we have here so far.
![y=\frac{1}{2}x +b](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx%20%2Bb)
All we have to do is find
.
The question wants the line to pass the point (-5, -1).
Let's plug that point in.
![-1=\frac{1}{2} (-5)+b\\-1=\frac{-5}{2}+b\\\frac{3}{2} =b\\](https://tex.z-dn.net/?f=-1%3D%5Cfrac%7B1%7D%7B2%7D%20%28-5%29%2Bb%5C%5C-1%3D%5Cfrac%7B-5%7D%7B2%7D%2Bb%5C%5C%5Cfrac%7B3%7D%7B2%7D%20%3Db%5C%5C)
We have all the information needed to finish this problem!
So, the line that is parallel to
and passes through the point (-5, -1).
![y=\frac{1}{2}x+\frac{3}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B3%7D%7B2%7D)