To determine if the point (0, -3) is a solution to the inequality \( y > \frac{4}{5}x - 3 \), we need to evaluate the inequality at the coordinates of the point.
First, substitute \( x = 0 \) into the equation of the line:
\[ y = \frac{4}{5}(0) - 3 = -3 \]
The boundary line is \( y = \frac{4}{5}x - 3 \). Since \( (0, -3) \) corresponds to the point when \( x = 0 \), the point lies exactly on the boundary line.
The inequality \( y > \frac{4}{5}x - 3 \) means we are looking for values of \( y \) that are greater than the values on the boundary line. Since \( -3 \) is not greater than \( -3 \) (it is equal), the point (0, -3) does not satisfy the inequality.
Considering the possible answers:
- "Yes, because (0, -3) falls on the boundary line." (This is true, but does not indicate it is a solution since it needs to be greater.)
- "Yes, because (0, -3) falls within the shaded region." (False, it is on the boundary line, not within the shaded region.)
- "No, because (0, -3) falls on the boundary line." (This is correct since it does not satisfy the inequality.)
- "No, because (0, -3) falls within the shaded region." (False, it's on the boundary line.)
The correct answer is: No, because (0, -3) falls on the boundary line.