# The equation of line is -3y+4x=9. How do you write the equation of a line that is parallel to line and passes through the point (-12,6)?

Jun 3, 2016

$y - 6 = \frac{4}{3} \left(x + 12\right)$

#### Explanation:

We will be using the point gradient form as we already have a point which the line will go $\left(- 12 , 6\right)$ through and the word parallel means that the gradient of the two lines must be the same.

in order to find the gradient of the parallel line, we must find the gradient of the line which it is parallel to it. This line is $- 3 y + 4 x = 9$ which can be simplified into $y = \frac{4}{3} x - 3$. This gives us the gradient of $\frac{4}{3}$

Now to write the equation we place it into this formula
$y - {y}_{1} = m \left(x - {x}_{1}\right)$, were $\left({x}_{1} , {y}_{1}\right)$ are the point which they run through and m is the gradient.