# What is the equation of the line perpendicular to y=-3/16x  that passes through  (-2,4) ?

Jun 7, 2016

If lines are perpendicular then the one slope is the negative reciprocal of the other. this means that ${m}_{1} \times {m}_{2} = - 1$

In this case ${m}_{1} = - \frac{3}{16}$
The perpendicular slope to this is $\frac{16}{3}$

Now we have the slope and we also have a point (-2,4).

Use the formula $y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - 4 = \frac{16}{3} \left(x - \left(- 2\right)\right) \text{ } \Rightarrow y - 4 = \frac{16}{3} \left(x + 2\right)$

$y = \frac{16}{3} x + \frac{32}{3} + 4$

$y = \frac{16}{3} x + 14 \frac{2}{3}$