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Lesson 14: Graphing Linear Inequalities in Two Variables (Alg1.2.21)

Author:Brenda Jiménez, IM Algebra 1, Geometry, Algebra 2 , GeoGebra Classroom Activities
Toolbar ImageMath Talk

Here is an expression: 2x+3y.

Decide if the values in each ordered pair, , make the value of the expression less than, greater than, or equal to 12.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)
Toolbar ImageSolutions and Not Solutions

Here are four inequalities:

Study each inequality assigned to your group and work with your group to:
  • Find some coordinate pairs that represent solutions to the inequality and some coordinate pairs that do not represent solutions.
  • Plot both sets of points. Either use two different colors or two different symbols like X and O.
  • Plot enough points until you start to see the region that contains solutions and the region that contains non-solutions. Look for a pattern describing the region where solutions are plotted.

x≥y

-2y≥-4

3x<0

x+y>10

Toolbar Image Sketching Solutions to Inequalities

Here is a graph that represents solutions to the equation

Sketch 4 quick graphs representing the solutions to each of these inequalities using the applets below. Drag the red points to adjust the line, select a line style from the dropdown menu, and select on the blank areas on the graph to shade them in.

x-y<5

x-y≤5

x-y>5

x-y≥5

For each graph, write an inequality whose solutions are represented by the shaded part of the graph.

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