Question

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

Answer 1

3x=2-3y

y=-x-3

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula

to find the line parallel to

Answer 2

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

`\text { slope }=\frac{-\mathrm{x} \text { coefficient }}{\mathrm{y} \text { coefficient }}=(-3)/(3)=-1`

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

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

Where "m" is the slope of the line

`\text { Here in our problem, } m=-1,\left(x_(1), y_(1)\right)=(3,-6)`

By substituting the values in point slope form we get,

`\begin{array}{l}{\rightarrow y-(-6)=-1(x-3)} \\\\ {\rightarrow y+6=-1(x-3)} \\\\ {\rightarrow y=-x-3}\end{array}`

Hence the required equation is y = -x - 3