Question

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

Answer 1

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 = `(6-2x)/3`

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

If we let x = 2, then "y" would equal `2/3`

y = `(6-2(2))/3`

y = `(6-4)/3`

y = `(2)/3`

This tells us that one of the points on our graph is
x = 2 , y = `2/3`
or ( 2, `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 `10/3`

y = `(6-2(-2))/3` [Remember -2 * -2 is +4]

y = `(6+4)/3`

y = `(10)/3`

So, x = -2, y = `10/3`
or ( -2, `10/3` )
or ( -2, 3.33) [approximately]