Question

A coordinate plane shows a graph of an upward-sloping, diagonal, dashed line, with shading extending from the line to the left. The line starts in quadrant 3, extends through quadrant 4, and ends in quadrant 1.
Is the point (0,−3)
a solution to the inequality y>45x−3
, as shown on the graph?

(1 point)
Responses

No, because (0,−3)
falls within the shaded region.
No, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.

No, because (0,−3)
falls on the boundary line.
No, because left parenthesis 0 comma negative 3 right parenthesis falls on the boundary line.

Yes, because (0,−3)
falls within the shaded region.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.

Yes, because (0,−3)
falls on the boundary line.

Answer 1

To determine whether the point \((0, -3)\) is a solution to the inequality \(y > 45x - 3\), we first evaluate the line defined by the equation \(y = 45x - 3\).

1. **Substituting the x-coordinate**: For \(x = 0\):
\[
y = 45(0) - 3 = -3
\]
This indicates that the point \((0, -3)\) lies exactly on the boundary line \(y = 45x - 3\).

2. **Understanding the inequality**: The inequality \(y > 45x - 3\) indicates that solutions are those points that are above the line \(y = 45x - 3\). Since the boundary line itself is dashed, the points on the line are not included as solutions.

3. **Conclusion on the point**: Since \((0, -3)\) lies on the dashed boundary line and the region above the line is shaded, the point itself is not a solution to the inequality \(y > 45x - 3\).

From the given options, the correct response is:

**No, because (0,−3) falls on the boundary line.**