Question

Is the point (0,−3)
a solution to the inequality y>45x−3
, as shown on the graph?

(1 point)
Responses

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

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.

Answer 1

To determine if the point (0, -3) is a solution to the inequality \(y > 45x - 3\), we should first evaluate the right-hand side of the inequality for \(x = 0\).

Plugging in \(x = 0\) into the equation \(y = 45x - 3\):

\[
y = 45(0) - 3 = -3
\]

Now we compare this with the y-coordinate of the point (0, -3):

- The point (0, -3) corresponds exactly with \(y = -3\) on the boundary line of the inequality.

Since the inequality is strict \(y > 45x - 3\), this means that points on the boundary line (where \(y = 45x - 3\)) are **not** included in the solution set.

Therefore, the correct response is:

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