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Graphing inequalities

System of Inequalities:
Graph the following: 2x+3y>6

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Apr 12, 2010
Graphing Inequalities
by: Karin

You originally titled your submission, Systems of Inequalities. In order to be classified as a system of inequalities, you must have 2 inequalities. You have one equality; therefore, this is not a system of inequalities.

To graph 2x + 3y > 6, you can either find the intercepts to plot your points or you can rewrite the equation in slope intercept form. For this problem, I find that finding the intercepts is easiest, but I find that many students rewrite the inequality in slope intercept form because that method is the most often used.

I will demonstrate how to find the intercepts.

Think of the inequality as an equation, just to find the intercepts.
2x + 3y = 6

To find the x -intercept let y = 0.
2x + 0 = 6
2x = 6
2x/2 = 6/2
x = 3

The x - intercept is 3. Therefore, you will plot a point on (3,0)

Now, let's find the y-intercept. To find the y-intercept, let x = 0.

0 + 3y = 6
3y = 6
3y/3 = 6/3
y = 2

The y-intercept is 2. Therefore, you will plot your second point on (0,2).

Now you will draw a DOTTED line through these two points. You are drawing a dotted line because your inequality symbol is >. If it were greater than or equal to, then you would draw a solid line.

Now, we will decide which side of the line to shade.
2x + 3y >6

Let's substitute the point (0,0).
2(0) +3(0) > 6

When we substitute (0,0), our statement reads:
0 is greater than 6. This statement is not true, so we will NOT shade the side of the line that contains (0,0). Instead we will shade the other side of the dotted line.

For more information on graphing inequalities, please visit:


I hope this helps!


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