Question

Decide whether the graphs of \(y=x+2\) and \(y=x-4\) are parallel lines.

Short answer

Yes, the graphs of \(y=x+2\) and \(y=x-4\) are parallel lines because they have the same slope.

Step-by-step solution

Identify the Slopes

The slopes of the lines \(y=x+2\) and \(y=x-4\) can be found by looking at the coefficient of \(x\) in each equation. In both cases, the slope is 1.

Compare the Slopes

Since the slopes are both 1, this means the lines are parallel.