Cogito
Algebra 1 · Chapter 2 · Lesson 5
Inequalities in Two Variables
A whole region of the plane, not a line.
11 problems · about 23 minutes · A-REI.D.12
What this lesson teaches
The student graphs a linear inequality in two variables and tests points against it.
- A linear inequality in two variables is satisfied by half the plane.
- The boundary is solid when equality is included and dashed when it is not.
- Testing one point off the line decides which side to shade.
Warm Up
Straightforward practice. Get the method working first.
4 problemsDoes (0, 0) satisfy y < x − 3? 1 for yes, 0 for no.
Answer 0
Why No.
y > x + 2. Is the boundary dashed? 1 for yes, 0 for no.
Answer 1
Why Strict.
Does (0, 0) satisfy y > x + 2? 1 for yes, 0 for no.
Answer 0
Why 0 > 2 is false.
Does (0, 5) satisfy y > x + 2? 1 for yes, 0 for no.
Answer 1
Why 5 > 2.
Build It Up
The same ideas with more to keep track of.
3 problemsy ≥ 2x. Is the boundary solid? 1 for yes, 0 for no.
Answer 1
Why Includes equality.
Order the steps for graphing a linear inequality.
Answer 1. Graph the boundary line 2. Make it solid or dashed 3. Test a point off the line 4. Shade the side that works
Why The test decides the shading, so it comes before it.
Does (2, 1) satisfy y < x? 1 for yes, 0 for no.
Answer 1
Why 1 < 2.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsCan the origin be used as a test point for y < x? 1 for yes, 0 for no.
Answer 0
Why The line passes through it.
How many points satisfy a linear inequality in two variables? Use 99 for infinitely many.
Answer 99
Why A whole region.
Testing a Point: Does (0, 0) satisfy y < 2x + 1? 1 for yes, 0 for no.
Answer 1
Why Yes.
The Line Style: For y ≤ 3x, is the boundary solid? 1 for yes, 0 for no.
Answer 1
Why Solid.