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Mr. Hernandez plotted the point (1, 1) on Han’s graph of y ≤ x + 2. He instructed Han to add a second inequality to the graph that would include the solution (1, 1). Which equation could Miguel write?

Respuesta :

The solution set of an inequality is given by the data points with the region

specified by the inequality.

The graph Miguel could write is y ≤ 2·x - 1.

Reasons:

The point Mr. Hernandez plotted = (1, 1)

Han's graph inequality = y ≤ x + 2

Required:

To select the inequality equation that include a solution of (1, 1)

Solution;

The inequality graph will have a solution of (1, 1), includes the point (1, 1) in

the solution set;

The possible options are;

y ≤ 2·x - 1

y ≥ 2·x + 1

y < 2·x - 1

y > 2·x + 1

At x = 1

  • y ≤ 2·x - 1 gives; y ≤ 2×1 - 1 = 1. ∴ When x = 1, y ≤ 1, the inequality y ≤ 2·x - 1 has (1, 1) as a solution
  • y ≥ 2·x + 1 gives; y ≥ 2×1 + 1 = 3. ∴ When x = 1, y ≥ 3, the inequality y ≥ 2·x + 1 has no solution at point (1, 1).
  • y < 2·x - 1 gives; y < 2×1 - 1 = 1. ∴ When x = 1, y < 1, the inequality y < 2·x - 1 has no solution at point (1, 1)
  • y > 2·x + 1 gives; y > 2×1 + 1 = 3. ∴ When x = 1, y > 3, the inequality y > 2·x + 1 has no solution at point (1, 1)

Therefore;

The graph Miguel could  write is y ≤ 2·x - 1

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Answer:

Its D, trying to save some time for you :)

Step-by-step explanation:

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