Question

What is the ordered pairs that satisfy the equation `3x - 2y = 6`?

Answer 1

You can find as many ordered pairs as you want.

Here are some:
`(6,6)`
`(2,0)` `larr` This is the `x` intercept
`(0,- 3)` `larr` This is the `y` intercept
`(-2,-6)`
`(-6,-12)`

Explanation:

You can write this line in slope-intercept form and use that equation to generate as many ordered pairs as you want.

`3x - 2y = 6`
Solve for `y`

1) Subtract `3x` from both sides to isolate the `-2y` term
`-2y = -3x + 6`

2) Divide both sides by `- 2` to isolate `y`
`y = (3x)/(2) - 3`

Now assign various values to `x` and solve for `y` to generate as many ordered pairs as you want.

Hot tip: Since you'll be dividing `3x` by `2`, choose only even numbers for `x`

... `x` .... | ... `y` ... | . .Ordered Pairs
.............|.............|...................................
... `6` ......| .... `6` ...| . . . `(6,6)`
... `2` ......| .... `0` ...| . . . `(2,0)` `larr` This is the `x` intercept
... `0` ......|. `-3` ...| . . . (0,⎯ 3)`larr` This is the `y` intercept
`-2` ......|. `-6` ...| . . . `(⎯ 2,⎯ 6)`
`-6` ......|. `-12` .| . . . `(⎯ 6,⎯ 12)`