Lesson 20Graphing Linear Inequalities in Two Variables (Part 1)
Learning Goal
Let’s find out how to use graphs to represent solutions to inequalities in two variables.
Learning Targets
Given a two-variable inequality and the graph of the related equation, I can determine which side of the line the solutions to the inequality will fall.
I can describe the graph that represents the solutions to a linear inequality in two variables.
Warm Up: Math Talk: Less Than, Equal to, or More Than 12?
Problem 1
Here is an expression:
Decide if the values in each ordered pair,
Activity 1: Solutions and Not Solutions
Problem 1
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.
Activity 2: Sketching Solutions to Inequalities
Problem 1
Here is a graph that represents solutions to the equation
Sketch 4 quick graphs representing the solutions to each of these inequalities:
Problem 2
For each graph, write an inequality whose solutions are represented by the shaded part of the graph.
Are you ready for more?
Problem 1
The points
Compute
for both of these points. Which point comes closest to satisfying the equation
? That is, for which pair is closest to 3?
Problem 2
The points
Problem 3
Find a point in the solution region that comes even closer to satisfying the equation
Problem 4
For the points
Problem 5
Find
Lesson Summary
The equation
We can represent all the solutions to
The graph is a line. All the points on the line are solutions to
The inequality
This means it includes all the pairs that are solutions to the equation
On a coordinate plane, the solution to
We can shade that region on one side of the line to indicate that all points in it are solutions.
What about the inequality
The solution is any pair of and whose sum is less than 7. This means pairs like
On a coordinate plane, the solution does not include points on the line that represent
To exclude points on that boundary line, we can use a dashed line.
All points below that line are