Which points are solutions to the linear inequality y ≤ 5x + 2? Check all that apply.

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Understanding the Linear Inequality

The inequality y ≤ 5x + 2 represents all the points (x, y) that are either on the line defined by the equation y = 5x + 2 or located below this line on a graph. To find the solutions, we need to test various points to see if they satisfy this condition.

Testing Points

Let’s consider a few example points:

  • A (0, 0)

    • Substituting x = 0 into the inequality: y ≤ 5(0) + 2 → y ≤ 2. Since 0 ≤ 2, point (0, 0) is a solution.

  • B (1, 6)

    • Substituting x = 1 into the inequality: y ≤ 5(1) + 2 → y ≤ 7. Since 6 ≤ 7, point (1, 6) is a solution.

  • C (-1, 3)

    • Substituting x = -1 into the inequality: y ≤ 5(-1) + 2 → y ≤ -3. Since 3 ≤ -3 is false, point (-1, 3) is not a solution.

  • D (2, 9)

    • Substituting x = 2 into the inequality: y ≤ 5(2) + 2 → y ≤ 12. Since 9 ≤ 12, point (2, 9) is a solution.

Summary of Solutions

Based on the above evaluations, the points that are solutions to the inequality y ≤ 5x + 2 are:

  • (0, 0)
  • (1, 6)
  • (2, 9)

Keep in mind, any point below the line defined by y = 5x + 2 will also satisfy the inequality. So, feel free to check any other points as needed!

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