Use the image to answer the question.

To determine whose graph is correct based on the information provided about the plotted points and the coordinates (−174, −2.5), we need to analyze the quadrants and values.

1. Understanding Quadrants:
   • Quadrant I: (x > 0, y > 0)
   • Quadrant II: (x < 0, y > 0)
   • Quadrant III: (x < 0, y < 0)
   • Quadrant IV: (x > 0, y < 0)

The point (−174, −2.5) is located in Quadrant III because both coordinates are negative (x < 0 and y < 0).

2. Analyzing Points:
   • Amy is in Quadrant II: (4.25, 2.5) - this is incorrect for (−174, −2.5).
   • Jacob is in Quadrant III: (3.4, 2.5) - this is incorrect for (−174, −2.5).
   • Rita is in Quadrant III: (4.25, 2.5) - this is incorrect for (−174, −2.5).
   • Leo is in Quadrant III: (2.5, 4.25) - this is incorrect for (−174, −2.5).

All three points in Quadrant III have positive x-values, while the required point has a negative x-value.

Thus, it seems none of the provided graphs accurately depict the point (−174, −2.5) given that all the plotted points in Quadrant III are incorrect for that coordinate.

Based on the given options, you might be looking for confirmation of Leo, Jacob, Amy, or Rita. Since the options do not include anyone who plotted a point close to (−174, −2.5) in Quadrant III, none of their graphs could be considered correct.

If I am to choose from the provided responses despite the inconsistencies:

• Jacob or Rita could be the closest in terms of quadrant, but since "None" is not an option, it appears all responses actually lead to incorrect plots for the specified point.

If forced to select from the responses according to the details provided in the question:

• Jacob and Rita are both in Quadrant III, but neither accurately represent the coordinates specified.

Final Answer: None of the students' graphs are correct for the point (−174, −2.5). If I must choose, I would suggest Jacob or Rita, considering they are in Quadrant III.

Based on the reasoning given and the quadrants in which the points lie, I would choose:

Jacob

His graph is at least in Quadrant III, which is the correct quadrant for the point (−174, −2.5), even though the specific coordinates do not match.

I apologize for any confusion in my previous messages. Upon reviewing the given information regarding the student's points:

• Jacob: (3.4, 2.5) - Quadrant III but x is positive
• Rita: (4.25, 2.5) - Quadrant III but x is positive
• Leo: (2.5, 4.25) - Quadrant III but x is positive
• Amy: (4.25, 2.5) - Quadrant II

None of the plotted points correspond correctly to (−174, −2.5), as they all are plotted with positive x-values, while the required point has a negative x-value.

Since I initially indicated that Jacob's placement in Quadrant III could make it a possible choice despite the x-value being incorrect, I understand your need for clarity.

If I must select just one based on being in the correct quadrant, I would reiterate:

Jacob

I recognize that this point selection is ultimately flawed based on the provided coordinates. None of the graphs accurately represent the point (−174, −2.5). Thank you for your patience!