Shading half of the plane to show the solution set.
Let's do these two things one at a time.
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. Also, the inequality is strict, so the points on the boundary line are not included in the solution set. We show this by drawing a dashed line.
Shading the Plane
The inequality x<-4 describes all values of x that are less than -4. This means that every possible (x,y) coordinate pair with an x-value that is less than -4 needs to be included in the shading.
Determining the Solutions
Finally, we can check the given points to see which ones are contained in the solution set. We will do this by adding the list of points to our coordinate plane.
Points that lie within the shaded region are solutions to the inequality. Note that points that lie on the dashed line are not solutions. This means that one of the given points is part of the solution set.
(-5, -5)
