Question

Are the following lines parallel, perpendicular, or neither? Explain. 3x+2y=7 and 4x-6y=-8

Answer 1

Given the lines:

`\begin{gathered} 3x+2y=7 \\ 4x-6y=-8 \end{gathered}`

We express them in slope-intercept form:

`\begin{gathered} 3x+2y=7\Rightarrow2y=7-3x\Rightarrow y=-(3)/(2)x+(7)/(2) \\ \\ 4x-6y=-8\Rightarrow6y=4x+8\Rightarrow y=(2)/(3)x+(4)/(3) \end{gathered}`

The slopes of these lines are:

`\begin{gathered} m_1=-(3)/(2) \\ m_2=(2)/(3) \end{gathered}`

Then:

`m_1\cdot m_2=-1`

This is the condition for perpendicular lines, so the lines are perpendicular.