Answer:
[tex]y=\frac{1}{2}x+\frac{3}{2}[/tex]
Step-by-step explanation:
Let's write [tex]-2x+4y=8[/tex] to slope-intercept form.
We do this by solving for [tex]y[/tex]
[tex]-2x+4y=8\\[/tex]
Add 2x to both sides
[tex]4y=8+2x[/tex]
Divide both sides by 4
[tex]y=\frac{1}{2} x+2[/tex]
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 [tex]\frac{1}{2}[/tex].
Slope-intercept form: [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
So, let's see what we have here so far.
[tex]y=\frac{1}{2}x +b[/tex]
All we have to do is find [tex]b[/tex].
The question wants the line to pass the point (-5, -1).
Let's plug that point in.
[tex]-1=\frac{1}{2} (-5)+b\\-1=\frac{-5}{2}+b\\\frac{3}{2} =b\\[/tex]
We have all the information needed to finish this problem!
So, the line that is parallel to [tex]-2x+4y=8[/tex] and passes through the point (-5, -1).
[tex]y=\frac{1}{2}x+\frac{3}{2}[/tex]
