Question

How do you decide whether the graphs of the two equations are parallel lines: `y=2x-1, y=-2x+1`?

Answer 1

Not parallel

Explanation:

Lines are parallel, if their slope is same.

Slope of y= 2x-1 is 2
Slope of y= -2x+1 is -2.

The slopes are not same (not equal), hence lines are not parallel

Answer 2

Both lines are expressed in slope intercept form `y=mx+p` where `m` is the slope.

To be parallel they would have to have the same slope. This is not the case so they are not parallel.

Explanation:

More in detail if the two lines

`y=2x-1`
`eta=-2x+1`

were parallel, then `y-eta` would be constant.

But:

`y-eta = 2x-1-(-2x+1) =4x-2`

and it is also obvious that the two lines cross for `x=1/2`