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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