Question

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

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

Yes, because (0,−3)
falls on the boundary line.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls on the boundary line.

Yes, because (0,−3)
falls within the shaded region.

Answer 1

To determine if the point (0, -3) is a solution to the inequality \(y > 45x - 3\), we need to check a few things regarding the boundary line and the shaded region of the graph.

First, let's find out what the boundary line looks like:

1. Set \(y = 45x - 3\) to find the equation of the boundary line.

2. At \(x = 0\), we get:
\[
y = 45(0) - 3 = -3
\]
3. Therefore, the point (0, -3) lies on the boundary line.

Since the inequality is \(y > 45x - 3\), it means that the solution will be the region above the line (not including the line itself, as it is a strict inequality).

Now, since (0, -3) lies on the boundary line, it does not satisfy the inequality \(y > 45x - 3\) because the inequality does not include equality (it doesn't include points on the boundary line).

Based on this analysis, the correct response is:

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