The reasoning can be applied to several x-values. Applying it to all x-values creates the entire region below the line y=x.
The method to graph a linear inequality is similar to graphing a linear equation in slope-intercept form, but instead of a line, the graph of a linear inequality is an entire region.To graph the linear inequality
If the test point is a solution to the inequality, the region in which it lies contains the entire solution set. If not, the other region contains the solutions. To show the set, shade the appropriate region.
Here, test point (0,0) is a solution to the inequality.
The region containing (0,0) lies to the left of the boundary line. Thus, this region shows the solution set of the inequality.
The point does not lie inside the shaded region, so it's not part of the solution set.