Let's solve the inequality \( y > 4x - 17 \) for the point \( (12, 31) \).
First, substitute \( x = 12 \) into the expression on the right side:
\[ 4x - 17 = 4(12) - 17 \] \[ = 48 - 17 \] \[ = 31 \]
Now, we check the inequality:
The inequality states \( y > 4x - 17 \). In this case, \( y = 31 \) and \( 4x - 17 = 31 \).
Since \( 31 \) is not greater than \( 31 \), but rather equal to \( 31 \), the point does not satisfy the inequality.
Thus, the correct answer is:
C) No, because 31 is equal to 4 · 12 - 17.