You want your problem to look like the slope-intercept form: y=mx+b at the end.
1.Subtract 2x from each side and get 3y=-2x+6
2. Divide each side by 3 to get y alone, so y=-2/3X+2
3. -2/3 is your slope, and 2 is your y-intercept. m=-2/3 and b=2
To graph, start the line with your y-intercept.
1. Plot a dot two units on the positive side of the y-axis (because your y-intercept is a positive number) such that the first point on the line will be (0,2).
2. Slope equals rise over run so count down two units (because the 2 is negative in this equation) and to the right three units (the three is positive) from your first point and you will have your next point at (3,0).
3. To make a third point, repeat: count down two units and three to the right from your second point, such that your next point is at (6,-2). Draw a straight line to connect the three points and there you have your graph!