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

Dec 5, 2016

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

Dec 5, 2016

Both lines are expressed in slope intercept form $y = m x + p$ 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

$y = 2 x - 1$
$\eta = - 2 x + 1$

were parallel, then $y - \eta$ would be constant.

But:

$y - \eta = 2 x - 1 - \left(- 2 x + 1\right) = 4 x - 2$

and it is also obvious that the two lines cross for $x = \frac{1}{2}$