# How do you write an equation of the line given (3,-6) with slope -4/3?

Aug 24, 2017

$3 y = - 4 x - 6$

#### Explanation:

The equstion of a straight line with slope $\left(m\right)$ passing through the point $\left({x}_{1} , {y}_{1}\right)$ is given by:

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

In our example: $m = - \frac{4}{3} \mathmr{and} \left({x}_{1} , {y}_{1}\right) = \left(3 , - 6\right)$

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

$3 \left(y + 6\right) = - 4 \left(x - 3\right)$

$3 y + 18 = - 4 x + 12$

$3 y = - 4 x + 12 - 18$

$3 y = - 4 x - 6$