# How do you graph the equation 2x+3y=6?

Apr 23, 2017

graph{2x+3y=6 [-10, 10, -5, 5]}

#### Explanation:

You can start by solving for "y".

2x + 3y = 6 [Subtract 2x from both sides]

3y = 6 - 2x [Divide both sides by 3]

y = $\frac{6 - 2 x}{3}$

Now we can assign values to "x" in order to get "y".
Like this.

If we let x = 2, then "y" would equal $\frac{2}{3}$

y = $\frac{6 - 2 \left(2\right)}{3}$

y = $\frac{6 - 4}{3}$

y = $\frac{2}{3}$

This tells us that one of the points on our graph is
x = 2 , y = $\frac{2}{3}$
or ( 2, $\frac{2}{3}$ )
or ( 2, 0.67) [approximately]

Keep giving "x" values until you have the graph that you need. I like to use the numbers -2, -1, 0, 1, and 2. Those five values for "x" should be enough to give you a nice graph. I'll do one more.

If we let x = -2, then "y" would equal $\frac{10}{3}$

y = $\frac{6 - 2 \left(- 2\right)}{3}$ [Remember -2 * -2 is +4]

y = $\frac{6 + 4}{3}$

y = $\frac{10}{3}$

So, x = -2, y = $\frac{10}{3}$
or ( -2, $\frac{10}{3}$ )
or ( -2, 3.33) [approximately]