Question

In the following exercises, use slopes and $y$-intercepts to determine if the lines are parallel, perpendicular, or neither.

$y=-1$ and$y=2$

Short answer

Lines $y=2$and $y=-1$ are parallel lines.

Step-by-step solution

Step 1. Use the definitions of parallel and perpendicular lines 

• Two lines that have the same slope are called parallel lines.
• Two lines that lie in the same plane and intersect at right angles are called perpendicular lines. The slopes of these two lines are negative reciprocals of each other. Their product is $-1$.

Step 2. Use the slope-intercept form 

The slope-intercept form is $y=mx+b$.

We can recognize that the lines $y=-1$and $y=2$ are horizontal lines and their slopes are both$0$.

Step 3.  Find the y-intercept

The horizontal lines cross the $y-$axis at $y=-1$and $y=2$.

So the $y-$intercepts are $(0,-1)$and $(0,2)$.

The lines have the same slope and different $y-$intercepts.

Therefore, these lines are parallel lines.