Dynamic Activity

Linear Inequalities

Problem 2 Graphing an Inequality in Two Variables

What is the graph of y > x − 2 ? bold italic y greater than bold italic x minus 2 question mark

First, graph the boundary line y = x − 2 . y equals x minus 2 .  Since the inequality symbol is > , greater than comma  the points on the boundary line are not solutions. Use a dashed line to indicate that the points are not included in the solution.

To determine which side of the boundary line to shade, test a point that is not on the line. For example, test the point (0, 0).

Because the point (0, 0) is a solution of the inequality, so are all the points on the same side of the boundary line as (0, 0). Shade the area above the boundary line.

✓ Got It?

2. What is the graph of y ≤ 1 2 x + 1 ? y less than or equal to , 1 half , x plus 1 question mark

Problem 3 Graphing a Linear Inequality in One Variable

What is the graph of each inequality in the coordinate plane?

1. x > − 1 bold italic x greater than negative 1

   Graph x = − 1 x equals negative 1  using a dashed line. Use (0, 0) as a test point.

   x > − 1 x greater than negative 1

   0 > − 1 ✓ 0 greater than negative 1 check mark

   Shade on the side of the line that contains (0, 0).

   

2. y ≥ 2 y greater than or equal to 2

   Graph y = 2 using a solid line. Use (0, 0) as a test point.

   y ≥ 2 y greater than or equal to 2

   0 ≥ 2 ✖ 0 greater than or equal to 2 u 2

   Shade on the side of the line that does not contain (0, 0).