The slopes of two lines are $\frac{5}{6}$ and $\frac{2}{p}$ .
Determine the value of $p$ that will make the lines
A) parallel
B) perpendicular
I understand how parallel lines have the same slope but different intercepts, and how lines that are perpendicular meet at right angles, but how do i go about finding the value of p for both?
Best Answer
A) The lines will be parallel to each other if their slopes/gradients are equal, hence we get
$$\frac{5}{6}=\frac{2}{p}\iff p=\frac{12}{5}$$
B) The lines will be perpendicular to each other if the product of their slopes/gradients is $-1$, hence we get $$\frac{5}{6}\times \frac{2}{p}=-1\iff p=\frac{-5}{3}$$