Interpreting graphs
Identify the situation that each graph could represent
The length of a necklace that you make at a rate of 10cm per hour without taking a break
The height of a balloon as it raises gets caught in a tree for a few minutes and then continues to rise
The first graph represents the length of a necklace being made without any breaks at a constant rate of 10cm/hour.
The second graph represents the height of a balloon that is rising but gets caught in a tree for a few minutes, causing the height to stop increasing. Once the balloon is freed, it continues to rise at a steady rate.
1. Graph 1 (length of a necklace): This graph could represent the situation of making a necklace continuously at a rate of 10 cm per hour without taking a break. The x-axis would represent the time in hours, and the y-axis would represent the length of the necklace in centimeters. The graph would show a linear increase, starting from zero and increasing by 10 cm every hour.
2. Graph 2 (height of a balloon): This graph could represent the situation of a balloon that is initially rising but then gets caught in a tree for a few minutes and continues to rise afterward. The x-axis would represent time, and the y-axis would represent the height of the balloon in meters. The graph would show an initial increase in height, followed by a horizontal flat line (representing the time the balloon is caught in a tree), and then a continued increase in height once the balloon is free from the tree.
To interpret the graphs for both situations, we need to consider the variables involved and the pattern they depict.
1) The length of a necklace that you make at a rate of 10cm per hour without taking a break:
In this scenario, the graph would have Time (hours) on the x-axis and Length of the necklace (cm) on the y-axis. The graph would show a linear increase, starting at the origin (0, 0) with a slope of 10 (since the necklace is made at a rate of 10cm per hour) and continuing to rise steadily and linearly without any breaks or interruptions.
2) The height of a balloon as it raises, gets caught in a tree for a few minutes, and then continues to rise:
Here, the graph would have Time (minutes) on the x-axis and Height of the balloon (meters) on the y-axis. The graph would have two distinct segments - a steady increase representing the balloon's ascent until it gets caught in the tree, followed by a short period of stability where the height remains constant while the balloon is stuck, and then another steady increase as it continues rising after the interruption.
To summarize:
1) The necklace-making graph would show a continuous linear increase.
2) The balloon's height graph would have an initial increasing segment, followed by a flat segment during the time it gets caught in the tree, and then a continuous increasing segment again once it continues rising.