How can we use the concept:
Graphing Inequalities on a Number Line:
When graphing an inequality on a number line, there are certain rules to keep each specific inequality distinct. We use shading and open/closed circles to denote direction and inclusion within the solution set.
Graphing Inequalities on a Coordinate Plane:
Graphing inequalities in two variables is shown on a coordinate plane. The graph is shaded either above/ right or below/left of the boundary line. The boundary line is dashed in a strict inequality: > and <
The boundary is solid if the inequality can also include the boundary: ≥ and ≤
For example, take the graph:
y>-2x+1
It is a strict inequality, thus the boundary line y=-2x+1 is dashed, and not solid. Since the inequality is greater than the boundary line, the points to the right/ above the boundary are shaded.
Sample Math Problems
1. Let’s look at the inequality 7x>14. In order to graph this on the numberline, we must first solve for x.
Solution:
While most inequalities can be solved in this straightforward manner, negatives affect the direction of the inequality sign. This means that if you multiply by a negative number then the inequality sign MUST BE flipped.
Let’s look at the same inequality, except now,
7-> -7
2. The coordinate plane is used to graph inequalities where there are two variables involved. We can describe a graph in the coordinate plane as a linear inequality.
Let’s look at the following graph:
First we find the boundary line. The line crosses the y-axis at y=-5, so there is one point (0,-5). This means b=-5. The boundary line also goes through the point (2,1) so now we can find the equation of that line.
3. Now let’s graph an inequality from an equation.
Let's use the inequality:
Solution:
First, graph the boundary line
