Graphing systems of inequalities and checking solutions

The  exercise appears under the Algebra I Math Mission. This exercise practices creating systems linear inequalities on the coordinate plane and testing points to see if they satisfy the system.

Types of Problems
There is one type of problem in this exercise:


 * 1) Graph the system and determine solutions: This problem provides an system of inequalities and a couple of points that may be solutions to the system. The student is asked to graph the system and determine which (if any) of the points are correct solutions.Gassoi1.png

Strategies
Knowledge of linear inequalities and graphing would ensure success on this exercise.
 * 1) Solid lines are used when the inequality could be equal to, dashed lines are for strict inequality.
 * 2) When a line is in slope-intercept form, shading is above the line when it is > and the shading is below when it is <.
 * 3) When a line is in standard form, the shading is the same as it is in slope-intercept form if the coefficient of the y-variable is positive, otherwise it is reversed (because there would be a "division" by a negative number to isolate y).
 * 4) A way to increase speed is to make a habit. For example, determine two points on the line, then determine solid or dashed, the determine side. Habits will decrease the chance of forgetting a step on this rather lengthy process.
 * 5) When working with standard form, it is sometimes necessary to choose better numbers to ensure the graph is precise. The manipulative essentially requires integer answers.
 * 6) Determining whether the points work or not can sometimes be determined by observing the quadrant the point is in.
 * 7) Be careful, sometimes the test point is actually on the line, in which case it works if the line is solid, but not if the line is dashed.

Real-life Applications

 * 1) Inequalities are far more valuable in real-life since real-life is not always exact.
 * 2) Linear inequalities are extremely useful in linear programming applications.