Answer:
[tex]y=\frac{1}{2}x+6[/tex] and [tex]y=5x+8[/tex]
Step-by-step explanation:
The big thing to remember with this is that parallel lines have the same slopes. We can isolate the y-variable in both of these to get the slope-intercept form, which just makes it easier to see the slope.
a. 3x-6y=12
[tex]-6y=-3x+12\\y=\frac{1}{2}x-2\\[/tex]
Now that we know the slope, we can have any y-intercept except for the original one, they just need to have the same slope. So an equation that could work is [tex]y=\frac{1}{2}x+6[/tex].
b. 5x-y=10
This equation can be solved in the exact same way.
[tex]-y=-5x+10\\y=5x-10[/tex]
Parallel line: [tex]y=5x+8[/tex]
Again, it does not matter what the y-intercept is, they just can't have the same one. The slopes have to be the same.
Hope this helps!
