Question

The equations of three lines are given below.Line 1: 2y-3x +42Line 2: y=-(2/3)x-7Line 3: 6x-4y=-2For each pair of lines, determine whether they are parallel, perpendicular, or neither.Line 1 and Line 2:O ParallelO Perpendicular ONeitherХhtLine 1 and Line 3:O ParallelO Perpendicular ONeitherLine 2 and Line 3: O ParallelO Perpendicular O Neither

Answer 1

Given three lines,

$\begin{gathered} 2y-3x+4=0 \\ y=-\frac{2}{3}x-7 \\ 6x-4y=-2 \end{gathered}$

Re- writing the above equations of the form, y=mx+c,

$\begin{gathered} y=\frac{3}{2}x-2 \\ y=-\frac{2}{3}x-7 \\ y=\frac{3}{2}x+\frac{1}{2} \end{gathered}$

Here the slope are as follows,

$\begin{gathered} m_1=\frac{3}{2} \\ m_2=-\frac{2}{3} \\ m_3=\frac{3}{2} \end{gathered}$

Since,

$m_1m_2=-1$

Line 1 and line 2 are perpendicular to each other.

$m_1=m_3=\frac{3}{2}$

Therefore, line 1 and line 3 are parallel to each other.

$m_2m_3=-1$

Line 2 and line 3 are perpendicular to each other.