Mathematicians, like magicians, artists, and other masters of the visual arts, communicate best when they accompany the abstractions they communicate with visual aids. It is a fact that the huge amount of people are visual learners. It is easy to graph simple linear equations on a number line. However, that isn’t the only way to visually depict a mathematical expression. By using a coordinate plane, it is again possible to plot the points of a linear expression. The coordinate plane is also useful for graphing inequalities. If the thought of graphing unequal equations sounds intimidating, breathe a sigh of relief. Although it is different from graphing expressions on a number line, it is every bit as simple.
Let’s start with an easy inequality. Graph y ≤ 2x – 4. Our goal is to find all the ordered pairs of x and y points that satisfy this expression. We’re really looking at two statements here, that y is = to 2x-4 and also, that y < 2x – 4. So, first you’d graph the straight line y = 2x – 4.
There are two ways to demonstrate the actual inequality contained in this expression. One,use a pencil to shade in the area of the solution. You’ve indicated the equals part with the line you’ve already graphed. Now, you just need to shade to one side or the other of the line to indicate the less than portion of the graph. If y is less than your line, you’ll want to shade below it.
Your second option is to use test points, and to plot them on your graph.Since you’ve already graphed what y is equal to, you now put your test numbers into the equation as x, and solve to find out what y is less than. No matter what your test numbers, you’ll find that your y values will all be less than those plotted on your equals to line.