To determine which inequalities the point (2, 2) satisfies, we will substitute \(x = 2\) and \(y = 2\) into each inequality and check if the inequality holds.
a) \(y < -2x + 1\)
Substituting \(x = 2\) and \(y = 2\):
\[ 2 < -2(2) + 1 \]
Calculating the right side:
\[ -2(2) + 1 = -4 + 1 = -3 \]
So the inequality is:
\[ 2 < -3 \quad \text{(False)} \]
b) \(y > 3x - 2\)
Substituting \(x = 2\) and \(y = 2\):
\[ 2 > 3(2) - 2 \]
Calculating the right side:
\[ 3(2) - 2 = 6 - 2 = 4 \]
So the inequality is:
\[ 2 > 4 \quad \text{(False)} \]
c) \(y > x - 1\)
Substituting \(x = 2\) and \(y = 2\):
\[ 2 > 2 - 1 \]
Calculating the right side:
\[ 2 - 1 = 1 \]
So the inequality is:
\[ 2 > 1 \quad \text{(True)} \]
Conclusion
The only inequality that (2, 2) satisfies is:
c) \(y > x - 1\)
So the answer is c only.