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 ≤ 5 & y = 5
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 a y-coordinate equal to 5. This means that it is a horizontal line. Notice that 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≤ 5 describes all values of y that are less than or equal to 5. This means that every possible (x,y) coordinate pair with a y-value that is less than or equal to 5 needs to be included in the shading.
