Find the missing rise that makes these lines perpendicular.

Question

The slopes of two lines are $m_1 = -3$ and $m_2 = k/4$.

Find the value of k that makes these lines perpendicular.

Answer 1

We know that 2 lines, $l_1$, $l_2$ with slopes $m_1$ and $m_2$ are perpendicular when $$m_1m_2=-1$$ Since it is given that $m_1=-3$ and $m_2=\frac{k}{4}$, $$-3\left(\frac{k}{4}\right)=-1$$ $$k=\frac{4}{3}$$ Therefore the value of $k$ that makes those lines perpendicular is $\frac{4}{3}$

Answer 2

If two lines are perpendicular, the product of their slopes is $-1$.

(For proof, see this question.)

Can you solve $-3k/4=-1$ for $k$?