Write equation that is parallel to 3x=2-3y and passes through (3,-6)

The equation of line that is parallel to 3x = 2 - 2y and passes through (3, -6) is y = -x - 3

Solution:

Given, line equation is 3x = 2 – 3y

⇒ 3x + 3y = 2 ⇒ (1)  

The point is (3, -6)

We have to find the equation of a line which is parallel to given line and passes through given point.

Now, let us find the slope of the given equation

So, slope of line is -1

We also know that, slopes of parallel lines are equal, then slope of our required line is – 1.

Then, let us find our line equation using point slope form

Where "m" is the slope of the line

By substituting the values in point slope form we get,

Hence the required equation is y = -x - 3