Paul's Online Notes
Paul's Online Notes
Home / Algebra / Graphing and Functions / Lines
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 3.2 : Lines

9. Determine if the line \(8x - y = 2\) and the line containing the two points \(\left( {1,3} \right)\) and \(\left( {2, - 4} \right)\) are parallel, perpendicular or neither.

Show All Steps Hide All Steps

Start Solution

To answer this question we’ll need the slope of each of the lines. For the first line let’s put the equation in slope-intercept form and get its slope.

\[\begin{align*}8x - y & = 2\\ y & = 8x - 2\hspace{0.25in}:\hspace{0.25in}{m_1} = 8\end{align*}\]

For the second line we can compute the slope directly from the two points.

\[{m_2} = \frac{{ - 4 - 3}}{{2 - 1}} = \frac{{ - 7}}{1} = - 7\] Show Step 2

The two slopes we found in the previous step are clearly not the same and so the two lines are not parallel. Also, we can see that \({m_1}{m_2} = - 56 \ne - 1\) and so the lines are also not perpendicular.

Therefore, the two lines are neither parallel nor perpendicular.