Question 345411
2x<3y+6


Treat the < sign as an equals sign, and rearrange the equation so that it looks like the equation of a line, y=mx+b


2x<3y+6


Subtract  6 from both sides:


2x-6 < 3y


Now divide both sides by 3:

(2x-6)/3 < y
2x/3 - 6/3 < y
2x/3 -2 < y


So comparing it to the equation of a line, this tells us that the slope is m=2/3 and the y-intercept is b=-2.


You can plot this on a graph by plotting the line of y=2x/3 -2, and then shading in the area underneath the line (because we were saying the inequality was showing everything that is less than y).

Here's a link to Wolfram Alpha's graph of it: http://www.wolframalpha.com/input/?i=2x-6+%3C+3y