Question

City planners want to construct a bike path perpendicular to Ravine Road at point P. An equation for the Ravine Road line is y= -2/7x. Find an equation for the line for the bike path.

Answer 1

Perpendicular lines have slopes that are negatiive reciprocals.

Ravine has a slope of -2/7

So, perpendicular line would have slope of 7/2

Hence, equation will be:

$y=\frac{7}{2}x+b$

We need a point, it is P, which is (0.0).

We substitute and find b:

$\begin{gathered} y=\frac{7}{2}x+b \\ 0=\frac{7}{2}(0)+b \\ 0=0+b \\ b=0 \end{gathered}$

Hence, final equation:

$y=\frac{7}{2}x$