To determine whether the point (0, -3) is a solution to the inequality \(y > 45x - 3\), we need to analyze the information provided about the graph.
- The line represented by the equation \(y = 45x - 3\) is dashed, indicating that points on the line are not included in the solution set (the inequality is strict).
- The shading extends from the line to the left, which indicates that all points to the left of the line satisfy \(y > 45x - 3\).
- The point (0, -3) lies on the y-axis.
To check if (0, -3) is above the line, substitute \(x = 0\) into the equation of the line:
\[y = 45(0) - 3 = -3.\]
Thus, the line at \(x = 0\) is \(y = -3\), which means that (0, -3) lies directly on the boundary line.
Since the line is dashed, (0, -3) is not included in the solution set for the inequality \(y > 45x - 3\).
Now, let's analyze the responses:
- "Yes, because (0,−3) falls within the shaded region." - Incorrect. (0, -3) is on the line, not in the shaded region.
- "Yes, because (0,−3) falls within the shaded region." - Same as above, incorrect.
- "Yes, because (0,−3) falls on the boundary line." - Incorrect for the inequality provided.
- "Yes, because (0,−3) falls on the boundary line." - Same reasoning is applied, incorrect.
- "No, because (0,−3) falls on the boundary line." - Correct. The point falls on the line and is not a solution to the inequality.
- "No, because (0,−3) falls within the shaded region." - Incorrect. It does not fall within the shaded region.
Thus, the correct response is: No, because (0,−3) falls on the boundary line.