Question

Determine whether the following pairs of lines are parallel, perpendicular, or neither. Write the corresponding letter on the line next to each problem: A = parallel, B = perpendicular, C = neither.

Answer 1

Solution

Write the equation whether it is parallel or perpendicular:

$\begin{gathered} y=-3x+2 \\ y=mx+c \\ m=-3 \\ m_1=-3 \end{gathered}$

To determine if the equation is perpendicular

$m_1m_2=-1$$\begin{gathered} (-5,6)\text{ and (1 , 8)} \\ m_2=\frac{y_2-y_1}{x_2-x_1} \\ x_1=-5,x_2=1 \\ y_1=6,y_2=8 \end{gathered}$$\begin{gathered} m_2=\frac{8-6}{1--5} \\ m_2=\frac{2}{6}=\frac{1}{3} \end{gathered}$$\begin{gathered} m_1m_2=-1\ldots\text{.. for perpendicular} \\ m_1=-3 \\ m_2=\frac{1}{3} \\ m_1m_2=\frac{1}{3}(-3)=-1 \end{gathered}$

Therefore the system of equation is said to be perpendicular