Question

Write the equation of a line parallel to the line with the equation
a. 3x- 6y=12 b. 5x-y=10

Answer 1

`y=(1)/(2)x+6` and
`y=5x+8`

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

`-6y=-3x+12\\y=(1)/(2)x-2\\`

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
`y=(1)/(2)x+6`.

b. 5x-y=10

This equation can be solved in the exact same way.

`-y=-5x+10\\y=5x-10`

Parallel line:
`y=5x+8`

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!