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
y ≤ 4 &
y = 4
Notice that this equation is telling us that each and every point that lies on the line will have a y-coordinate equal to 4. This means that it is a horizontal line. Also the inequality is notstrict, so the points on the boundary line are included in the solution set. We have shown this by drawing a solid line.
Shading the Plane
The inequality y≤4 describes all values of y that are less than or equal to 4. This means that every possible (x,y) coordinate pair with a y-value that is less than or equal to 4 needs to be included in the shading.
