# How do you write an equation of a line given point (4, -1) and perpendicular to a line with equation 3x + y =4?

May 14, 2016

$y = 4 - 3 x \to$ the slope of this line is -3

The slope of a perpendicular line is the negative reciprocal , therefore $\frac{1}{3}$.

Now, using point slope form, $y - {y}_{1} = m \left(x - {x}_{1}\right)$, we get:

$y - \left(- 1\right) = \frac{1}{3} \left(x - 4\right)$

$y + 1 = \frac{1}{3} x - \frac{4}{3}$

$y = \frac{1}{3} x - \frac{7}{3}$

Hopefully this helps!