maureen is filling dozens of water balloons for a party. she notices that, as she fills each balloon, the…

Explanation:

Step1: Analyze the relationship

As the balloon is filled, volume (x - axis) and weight (y - axis) increase steadily until the balloon is full. After that, volume stops increasing, but the problem is about the weight in relation to its volume while filling (before it's full? Wait, no—the question is about the weight as volume increases until it's full. Wait, the first graph has a horizontal line after a point, meaning weight stops increasing when volume stops (after full). But when filling, as volume increases, weight increases. Wait, the process: when filling, volume and weight increase together. Once full, volume stops, but the question is "the weight of a water balloon in relation to its volume"—so while filling, volume increases, weight increases. But when the balloon is full, does volume stop? Wait, the first graph: when volume reaches a certain point, weight stops (horizontal line). The second graph: weight keeps increasing with volume. But in reality, when you fill a balloon, once it's full, you can't add more water, so volume stops, and weight stops. But the question is "as she fills each balloon, the volume and weight increase steadily. Once each balloon is full, she ties it off..." So the graph should show that as volume (x) increases, weight (y) increases, and when the balloon is full, volume stops, but the graph for the relation during filling—wait, maybe the first graph: when filling, volume increases, weight increases (the sloped part), then when full, volume can't increase, so weight can't increase (horizontal part). But the second graph has weight increasing indefinitely with volume, which isn't possible because a balloon has a maximum volume. Wait, but maybe the question is about the graph while filling, before it's full? No, the process is: filling (volume increases, weight increases) until full, then volume stops. So the graph should have a linear increase (since steady increase) and then a horizontal line. But the second graph has no horizontal line. Wait, maybe I misread. Wait, the two graphs: left graph (first) has a sloped line then horizontal. Right graph (second) has a sloped line continuing. But when filling, as volume increases, weight increases. Once full, volume stops, so weight stops. So the left graph (first) shows that: as volume increases, weight increases (slope), then when volume stops (full), weight stops (horizontal). But the question is "which graph could show the weight... in relation to its volume"—so during the filling process, volume and weight increase together, and when full, volume can't increase, so weight can't. So the left graph (first) has a sloped part (filling) and horizontal (full, volume stops, weight stops). But wait, maybe the problem is that when the balloon is full, the volume is at a maximum, but the graph is about the weight as a function of volume during filling. Wait, maybe the key is: "steady increase" means linear (constant rate), so the slope is constant. Then, when full, volume stops, so weight stops. So the first graph (left) has a linear increase (steady) then horizontal. The second graph has linear increase but no stop. But in reality, a balloon has a maximum volume, so the first graph is correct. Wait, but maybe the question is simpler: when filling, as volume increases, weight increases. Once full, volume doesn't increase, so weight doesn't. So the graph should have a line that goes up (sloped) and then flat. So the left graph (first) is the one. Wait, but let's check the axes. x is volume, y is weight. So when volume increases, weight increases (slope), then when volume can't increase (full), weight stays same (horizontal). So the left graph (the first one, with the horizontal segment) is correct. Wait, but maybe I made a mistake. Wait, the problem says "as she fills each balloon, the volume and weight increase steadily"—so during filling, volume and weight increase together (linear, steady). Once full, volume stops, so weight stops. So the graph should have a linear increase (slope) and then a horizontal line. So the left graph (first) has that. The right graph has no horizontal line, so it's incorrect. So the answer is the left graph (first one, the one with the horizontal segment after the slope).

Step2: Identify the correct graph

The left graph (first) shows a steady (linear) increase in weight with volume (sloped line) and then a horizontal line when the balloon is full (volume stops, weight stops). The right graph shows weight increasing indefinitely with volume, which is impossible for a balloon with a maximum volume. So the correct graph is the left one (first graph).

Answer:

The graph on the Left (the first graph, with the horizontal segment after the sloped line)