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

Answer 1

To determine if the point (0, -3) is a solution to the inequality \( y > 45x - 3 \), we first need to evaluate the inequality with \( x = 0 \):

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

Now, we can analyze the point (0, -3). The y-coordinate of the point is -3, which does not satisfy the inequality \( y > -3 \). In fact, it is on the boundary line \( y = -3 \).

Since the inequality is strictly greater than, the point (0, -3) is not a solution because it does not fall within the region where \( y \) is greater than -3.

Therefore, the correct response is:

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