Question

How do you graph the equation `3y – 2x = 6` on a coordinate plane?

Answer 1

Convert the equation `3y-2x=6`to slope-intercept form.

Add 2x to both sides.

`3y=2x+6`

Divide both sides by 3.

`y=2/3x+2`

The slope is `2/3` and the y-intercept is `2`.

Determine some points on the line by making x=0 and y=0.

If `x=0`:
`y=2/3*0+2`
`y=2`
Point = `(0,2)`

If `y=0`:
`0=2/3x+2`
`-2/3x=2`
Multiply times both sides by 3.
`-2x=6`
Divide both sides by -2.
`x=-3`
Point=`(-3,0)`

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

Answer 2

`3y-2x=6` is a straight line function
so the easiest way to graph it is to establish two points on the line.
In a case like this one the easiest two points to establish are the x and y intercepts.
By inspection
x-intercept occurs at `(-3,0)`
y-intercept occurs at `(0,2)`

Make these two points on a graph and draw the straight line that runs through both of them.