Let's graph each of the separately and then place the graphs on the same .
In order to graph an inequality we need the . A boundary line can be written by replacing the inequality symbol with an equals sign.
The boundary line of the inequality is which is a horizontal line whose is Notice that the line is solid because the inequality is not strict.
Since all values greater than or equal to are in the solution set, we will shade above the line.
To start, let's determine the boundary line.
Notice that the boundary line is in . In order to draw the line, we will plot the intercept and use the to determine a second point. Also, the boundary line will be solid because our inequality is non-strict.
Next, we will test a point. If the point satisfies the inequality, we shade the region that contains the test point. Otherwise, we will shade the other region. Let's test
Since the test point satisfies the inequality, we will shade the region that contains the test point. Let's add this graph to the same coordinate plane with Inequality (I).
In the same manner as before, let's determine the boundary line for Inequality (III).
Once again, let's test the point
Since the point satisfies the inequality, we will shade the region that contains the point. This boundary will be solid as well because the inequality is not strict. Let's add it to the same coordinate plane as the first two inequalities.
Viewing the Solution
Next, let's remove all of the parts of the shading that aren't including in the overlapping sections.
Finding the Shape and its Area
The overlapping section is a triangle. To calculate its area, we need to determine the base and height.
Then we can use the formula for the .
As we can see from the graph,
Let's find the area.
As a result, the area is