Chapter 3.6, Problem 6YT

Determine whether the line given by $8x+y=2$

is parallel to the line given by $y=8x+7$.

Two lines are perpendicular if they intersect at a right angle. If one line is vertical and another is horizontal, they are perpendicular. There are other instances in which two lines are perpendicular.

Consider a line $\stackrel{\leftrightarrow }{RS}$

as shown at left, with slope $a/b$. Then think of rotating the figure $90°$ to get a line $\stackrel{\leftrightarrow }{R\text{'}S\text{'}}$ perpendicular to $\stackrel{\leftrightarrow }{RS}$. For the new line, the rise and the run are interchanged, but the run is now negative. Thus the slope of the new line is $-a/b$. Let’s multiply the slopes:

$\frac{a}{b}\left(-\frac{b}{a}\right)=-1$

This can help us determine which lines are perpendicular.