Wednesday, February 15, 2012

For those having problems figuring out the graphical solution of a linear inequality, I have a tip that will help.  Suppose you have the equation 3x + y < 6.  First subtract 3x from both sides of the equation to get y < -3x + 6.  From here you can graph the equation by plotting a point at (0, 6) and using the slope of -3 for another point. Draw a dotted line through the points as shown in the graph below.  The solution set will be all points either above or below this dotted line.  Pick a point that is NOT on the line and test in the equation to see if it is a true statement. The easiest point to pick is (0, 0). Substituting this into the equation we get 0 < -3(0) + 6, which is 0 < 6. This is a true statement. Therefore all the points on the same side of  the line as (0, 0)  is also in the solution set. Notice this region is shaded in yellow.

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