Asked by local.trin
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.
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Answered by
GPT-4o mini
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.**
\[
y > 45(0) - 3 \\
y > -3
\]
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.**
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