Lesson 21

From One- to Two-Variable Inequalities

  • Let’s look at inequalities in two dimensions.

21.1: Describing Regions of the Plane

For each graph, what do all the ordered pairs in the shaded region have in common?

A

Coordinate plane, x, negative 10 to 10 by 2, y, negative 10 by 10 by 2. Horizontal line drawn at y = 0. Plane shaded above the line y = 0.

B

Coordinate plane. Quadrants 2 and 3 shaded

C

Coordinate plane, quadrant 1 shaded 

D

Coordinate plane, quadrant 4 shaded 

21.2: More or Less

  1. Write at least 3 values for \(x\) that make the inequality true.
    1. \(x < \text{-}2\)
    2. \(x+2 > 4\)
    3. \(2x-1 \leq 7\)

  2. Graph the solution to each inequality on a number line.

    1. Blank number line, negative 10 to 10 by ones.
    2. Blank number line, negative 10 to 10 by ones.
    3. Blank number line, negative 10 to 10 by ones.

  3. Using the inequality \(x < \text{-}2\), write 3 coordinate pairs for which the \(x\)-coordinate makes the inequality true. Use the coordinate plane to plot your 3 points.

    Coordinate plane 

21.3: Above or Below the Line

  1. Graph the line that represents the equation \(y = 3x-4\)

    Coordinate plane 
  2. Is the point \((4,8)\) on the line?
    1. Explain how you know using the graph.
    2. Explain how you know using the equation.
  3. Use the 3 points \((5, a), (\text-7,b) \) and \((c,20)\)
    1. Write values for \(a, b,\) and \(c\) so that the points are on the line.
    2. Write values for \(a, b,\) and \(c\) so that the points are above the line.
    3. Write values for \(a, b,\) and \(c\) so that the points are below the line.

Summary