Linear Inequalities and Written Region Descriptions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Checking points and describing inequality regions

Mathematics · Algebra · ages 15-16
Name ______________________   Date ____________

  1. To decide which side of y = 3x to shade for y > 3x, which point can be used as a test point?

    • (0, 0)
    • (1, 3)
    • (0, 2)
    • (-1, -3)

  2. The region y less than 2x plus 1 is shaded. Should its boundary line be dashed or solid?

    • Dashed; the boundary is excluded
    • Solid; every boundary point is excluded
    • Solid; every boundary point is included

  3. For a single linear inequality, what does a solid boundary line tell you?

    • All points on it fail that inequality
    • All points on it satisfy that inequality
    • All points on it satisfy every inequality

  4. The point (0, 0) lies in the region y less than 2x plus 1.

    Circle one:   True   False

  5. A region is right of a solid line x = -1 and above a dashed line y = 2. Which pair of inequalities describes it?

    • x > -1 and y >= 2
    • x >= -1 and y > 2
    • x <= -1 and y > 2
    • x >= -1 and y < 2

  6. Sofia says the point (2, 5) lies in the region y less than 2x plus 1.

    Circle one:   True   False

  7. How many integer-coordinate points satisfy x >= 0, y >= 0 and x + y <= 3? Count allowed boundary points too.

    Answer: ______________

  8. How many integer-coordinate points satisfy x >= 0, y > 0 and x + y < 4?

    Answer: ______________

  9. How many integer-coordinate points satisfy 0 <= x <= 3 and 0 <= y <= 2? Count allowed boundary points too.

    Answer: ______________

  10. How many integer-coordinate points satisfy 0 <= x <= 2, y >= x and y <= 4 - x?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Checking points and describing inequality regions W1-mt_sKerzcAcNy-s1

  1. (0, 2) · A test point must be off the boundary. Only (0, 2) is off y = 3x. Its test is 2 > 0, so shade its side.
  2. Dashed; the boundary is excluded · A strict sign excludes its boundary, and excluded boundaries are dashed.
  3. All points on it satisfy that inequality · A solid boundary includes equality, so its points satisfy that inequality. Other inequalities in a system still need checking.
  4. True · Putting in zero gives 0 less than 1, which is true.
  5. x >= -1 and y > 2 · Right of x = -1 gives larger x-values, with equality for the solid boundary. Above y = 2 gives larger y-values, without equality for the dashed boundary.
  6. False · Putting in the point gives 5 less than 5, which is false.
  7. 10 · Including the allowed boundary points, the columns contain 4, 3, 2 and 1 points. Their sum is 10.
  8. 6 · Exclude y = 0 and x + y = 4. The nonempty columns contain 3, 2 and 1 integer points, totaling 6.
  9. 12 · Four integer x options times three integer y options gives 12 pairs.
  10. 9 · For x = 0, 1 and 2, the integer y counts are 5, 3 and 1. Their sum is 9.
Worksheet · LightMySky