Unit 7, Lesson 4
Graphing Linear Inequalities in Two Variables (Part 1)
Integrated Math 1
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Here are four inequalities. Study each inequality assigned to your group and work with your group to:
Here is a graph that represents solutions to the equation
Sketch 4 quick graphs representing the solutions to each of these inequalities:
AInequality graphed on a coordinate plane, origin O. Each axis from negative 10 to 8, by 2’s. Dashed line passes through 3 comma 8, 3 comma 0, and 3 comma negative 10. The region to the right of the dashed line is shaded.
BInequality graphed on a coordinate plane, origin O. Each axis from negative 10 to 8, by 2’s. Solid line passes through negative 10 comma negative 2, negative 2 comma negative 2, and 10 comma negative 2. The region below the solid line is shaded.
CInequality graphed on a coordinate plane, origin O. Each axis from negative 10 to 8, by 2’s. Dashed line passes through negative 10 comma negative 10, 0 comma 0, and 10 comma 10. The region above the dashed line is shaded.
DInequality graphed on a coordinate plane, origin O. Each axis from negative 10 to 8, by 2’s. Solid line passes through negative 10 comma negative 10, 0 comma 0, and 10 comma 10. The region below the solid line is shaded.
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.
Inequality graphed on a coordinate plane, origin O. Each axis from negative 8 to 10, by 2’s. Solid line goes through 0 comma 7 and 5 comma 2. The region below the solid line is shaded. The points negative 6 comma 0 and 4 comma negative 7 are labeled.
What about the inequality
The solution is any pair of
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
Inequality graphed on a coordinate plane, origin O. Each axis from negative 8 to 10, by 2’s. Dashed line goes through 0 comma 7 and 7 comma 0. The region below the dashed line is shaded.