Question

Is the point (0, - 3) a solution to the inequality y > 4/5 * x - 3 as shown on the graph?
Yes, because (0, - 3) falls on the boundary line.
Yes, because (0, - 3) falls within the shaded region.
No, because (0, - 3) falls on the boundary line.
No, because (0, - 3) falls within the shaded region.

Answer 1

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.**