Exercise 55 Page 669

We are asked to find the inequality that represents the given graph. There are two major steps we need to follow in order to write an inequality when given its graph.

1. Write an equation for the boundary line.
2. Determine the inequality symbol and complete the inequality.

Let's start by focusing on the boundary line.

Writing the Boundary Line Equation

Notice that all of the answers use the same equation for the boundary line in slope-intercept form. y= 1/3x+ 1 Since the boundary line equation is already given, we do not need to find it and we are ready to look for the inequality that represents the graph given in the exercise.

Forming the Inequality

To finish forming the inequality, we need to determine the inequality symbol. This means replacing the equals sign with a blank space, since it is still unknown to us. y ? 1/3x+1 To figure out what symbol should be used, we need a test point that lies within the solution set.

We will substitute ( 0, 0) for this test, then make the inequality symbol fit the resulting statement.

Zero is less than 1. We can infer that, of the four inequality symbols, only two would make this a true statement, < or ≤. Returning to the given graph one last time, we see that the boundary line is dashed. This implies that the inequality is non-strict. We can now form our final inequality. y < 1/3x+1 This corresponds to answer G.