# How do you write the equation in point slope form given slope of -1/3 and passing through the point (6, -4)?

Mar 25, 2016

$x + 3 y + 6 = 0$

#### Explanation:

the equation in point slope form slope of $- \frac{1}{3}$ and passing through the point $\left(6 , - 4\right)$

By slope point form,

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

$\left(y - \left(- 4\right)\right) = - \frac{1}{3} \left(x - 6\right)$

$\left(y + 4\right) = - \frac{1}{3} \left(x - 6\right)$

$y + 4 = - \frac{x}{3} + 2$

$y + \frac{x}{3} = 2 - 4$

$\frac{3 y + x}{3} = - 2$

$3 y + x = - 2 \times 3$

$3 y + x = - 6$

$3 y + x + 6 = 0$

i.e. $x + 3 y + 6 = 0$