# How do you write an equation of the line containing the given point (3,4) and perpendicular to y=3x+4?

Jun 5, 2018

If it is perpendicular to $y = 3 x + 4$ then it has a gradient of $- \frac{1}{3}$ because when you multiply the gradients together the answer is -1.

The line is of the form $y = - \frac{1}{3} x + c$ but it passes through (3,4)

$\implies 4 = - \frac{1}{3} \times 3 + c$

$4 = - 1 + c$

$c = 5$

$y = - \frac{1}{3} x + 5$