To graph the inequality, you have to draw the boundary line, then decide which side of the boundary line to shade.
Practice makes perfect
Graphing an inequality involves two main steps.
Plotting the boundary line.
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 ≥ -6 &
x = -6
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 -6. This gives us a vertical line. Also, the inequality is notstrict, so the points on the boundary line are included in the solution set. We show this by drawing a solid line.
The inequality x≥-6 describes all values of x that are greater than or equal to -6. This means that every possible (x,y) coordinate pair with an x-value that is greater than or equal to -6 needs to be included in the shading.
