In order to compare the differences between graphs of linear equations in two variables and linear inequalities in two variables, let's compare the graphs for functions that are nearly identical, that differ only in their symbols.
&y=2x+1
&y>2x+1
Let's first graph each of these functions individually and then make our comparison.
To graph this inequality, we need to first graph our boundary line. This is actually going to be the same line as our previous function. However, because our inequality is strictly comprised by values where y is greater than >, our line will be dashed, since points along this line are not included.
Now, we can show the entire solution set by adding some shading. To decide which side of the line to shade, we can substitute any point, such as (0,0).
Because (0,0) is not a solution to the inequality, we need to shade the side of the line that does not contain the origin.
Comparison
The graph of a linear equation is a straight line. Linear inequalities have graphs that shade the entire region on the adequate side of the boundary line. Moreover, depending on the inequality sign, the line can be solid or dashed.
