Question

Two nonvertical lines have slopes $m_1$and $m_2,$respectively. The lines are parallel if ______ and the ______ are unequal; the lines are perpendicular if ______.

Short answer

Two nonvertical lines have slopes $m_1$and $m_2$, respectively. The lines are parallel if $m_1=m_2$and the $y-$intercept; the lines are perpendicular if$m_1=-\frac{1}{m_2}$.

Step-by-step solution

Step 1. Given information.

We have:

Two nonvertical lines have slopes $m_1$and$m_2$ , respectively. The lines are parallel if ______ and the ______ are unequal; the lines are perpendicular if ______.

Step 2. Fill the blank. 

As we know that parallel lines are two straight lines that never touch.

Therefore, parallel lines have the same slope, but different $y-$intercepts.

Two non-vertical lines are perpendicular if and only if the product of their slopes is $-1$.

Therefore, the statement is "Two nonvertical lines have slopes$m_1$and$m_2$, respectively. The lines are parallel if$m_1=m_2$and the$y-$intercept; the lines are perpendicular if$m_1=-\frac{1}{m_2}$.