Q. 7 - Precalculus Enhanced with Graphing Utilities

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 ______.

Step-by-Step Solution

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 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 $m_1=-\frac{1}{m_2}$.