This week in Pre Calc 11 we learned how to graph linear inequalities in two variables. We recalled that a linear inequality is different from a quadratic inequality because linear means that it only has a degree of one. We also learned how to identify the y-intercept and the slope of a linear inequality. For example in the inequality: the y-intercept is the second term which is positive and the slope is the first term which has a rise of and a run of We also learned how to determine whether the boundry line of the linear inequality will be broken or solid. If the linear inequality is greater than, less than or equal to (includes), then the boundry line will be solid, however if it is only greater than or less than (excludes), then it will be broken. For example in the inequality: the inequality sign tells us that the value for must be greater than to make this inequality a true statement, this means that the boundry line for this inequality will be broken.

Once we learned how to determine the y-intercept, the slope and whether the boundry line will be broken or solid, we began to graph. In the first example we used, we know that the slope is the y-intercept is and that the boundry line will be broken. If we were to draw this linear inequality on a graph it would look like this:

Once we have graphed the linear inequality, we must determine the possible solutions that will satisfy the inequality by shading the one side of the graph. To determine which region will satisfy the inequality we choose points (called the test points) on either side of the boundry line and input them into the linear inequality. If the inequality sign is true to the numbers then shade in the region of those points, if not shade in the opposite region of the graph.

I have included an example below that shows the detailed steps I would take to determine which region on a graph to shade to find True possible solutions.