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Cogito

Algebra 1 · Chapter 2 · Lesson 5

Practice Worksheet

Inequalities in Two Variables

A whole region of the plane, not a line.

11 problems · about 23 minutes · A-REI.D.12

NameDate

Figure — use these to answer the problems

Set the boundary, then decide which side satisfies the inequality.
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y = 2x + 1
Slope2
Intercept1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Does (0, 0) satisfy y < x − 3? 1 for yes, 0 for no.

    Answer

  2. y > x + 2. Is the boundary dashed? 1 for yes, 0 for no.

    Answer

  3. Does (0, 0) satisfy y > x + 2? 1 for yes, 0 for no.

    Answer

  4. Does (0, 5) satisfy y > x + 2? 1 for yes, 0 for no.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. y ≥ 2x. Is the boundary solid? 1 for yes, 0 for no.

    Answer

  2. Order the steps for graphing a linear inequality.

    Write 1 to 4 in the boxes to put these in order.

    • Graph the boundary line
    • Make it solid or dashed
    • Test a point off the line
    • Shade the side that works

  3. Does (2, 1) satisfy y < x? 1 for yes, 0 for no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Can the origin be used as a test point for y < x? 1 for yes, 0 for no.

    Answer

  2. How many points satisfy a linear inequality in two variables? Use 99 for infinitely many.

    Answer

  3. Testing a Point

    Does (0, 0) satisfy y < 2x + 1? 1 for yes, 0 for no.

    Answer

  4. The Line Style

    For y ≤ 3x, is the boundary solid? 1 for yes, 0 for no.

    Answer