Shading half of the plane to show the solution set.
Boundary Line
To graph the inequality, we have to draw the boundary line. The equation of a boundary line is written by replacing the inequality symbol from the inequality with an equals sign.
Inequality
Boundary Line
x≤ 4
x=4
Notice that the equation for this boundary line only has one variable. This equation is telling us that each and every point that lies on the line will have an x-coordinate equal to 4. This gives us a vertical line. Notice that the inequality is notstrict, so the points on the boundary line are included in the solution set. We will show this by drawing a solid line.
Shading the Plane
The inequality x≤4 describes all values of x that are less than or equal to 4. This means that every possible (x,y) coordinate pair with an x-value that is less than or equal to 4 needs to be included in the shading.
