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

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=(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=(8-6)/(1--5) \\ m_2=(2)/(6)=(1)/(3) \end{gathered}`
`\begin{gathered} m_1m_2=-1\ldots\text{.. for perpendicular} \\ m_1=-3 \\ m_2=(1)/(3) \\ m_1m_2=(1)/(3)(-3)=-1 \end{gathered}`

Therefore the system of equation is said to be perpendicular