Graphs of proportions the image to answer the question.
A graph with x-axis and y-axis labeled from 0 to 30 in increments of 2. Three points are plotted with a line connecting them. A graph with x-axis and y-axis labeled from 0 to 30 in increments of 2. Points are plotted at (2, 10), (3, 15), and (6, 30). A line is drawn connecting the three points. The stretch of a spring in millimeters is proportional to the weight in grams attached to the end of the spring. Find the unit rate
The unit rate in this scenario would be the amount the spring stretches in millimeters for each gram of weight attached. To find the unit rate, we can calculate the change in stretch divided by the change in weight.
Using the given points, we can determine the change in stretch and weight:
- (2, 10): This point represents a weight of 10 grams and a stretch of 2 millimeters.
- (3, 15): This point represents a weight of 15 grams and a stretch of 3 millimeters.
- (6, 30): This point represents a weight of 30 grams and a stretch of 6 millimeters.
The change in stretch is 6 - 2 = 4 millimeters.
The change in weight is 30 - 10 = 20 grams.
Therefore, the unit rate is 4 millimeters per 20 grams, which simplifies to 0.2 millimeters per gram.
To find the unit rate, we need to determine how much the y-axis (stretch in millimeters) changes for every one unit increase on the x-axis (weight in grams).
First, let's identify the change on the y-axis given the change on the x-axis for each set of points:
From (2, 10) to (3, 15):
The change on the y-axis is 15 - 10 = 5 millimeters.
The change on the x-axis is 3 - 2 = 1 gram.
From (3, 15) to (6, 30):
The change on the y-axis is 30 - 15 = 15 millimeters.
The change on the x-axis is 6 - 3 = 3 grams.
Now, let's calculate the unit rate for each set of points:
For the first set of points:
Unit Rate = Change in y / Change in x
= 5 millimeters / 1 gram
= 5 millimeters/gram
For the second set of points:
Unit Rate = Change in y / Change in x
= 15 millimeters / 3 grams
= 5 millimeters/gram
As we can see, the unit rate for both sets of points is 5 millimeters/gram.
To find the unit rate in this scenario, we need to determine the ratio between the stretch of the spring in millimeters and the weight in grams attached to the end of the spring.
Looking at the graph, we can see that on the x-axis, we have the weight in grams, and on the y-axis, we have the stretch of the spring in millimeters.
The first point on the graph is (2, 10), which means that when a weight of 2 grams is attached to the spring, it stretches by 10 millimeters. The second point is (3, 15), indicating that when the weight is increased to 3 grams, the spring stretches by 15 millimeters. Finally, the third point is (6, 30), showing that for a weight of 6 grams, the spring stretches by 30 millimeters.
To calculate the unit rate, we can select any two points on the graph and find the ratio of the change in the stretch (difference in y-values) to the change in weight (difference in x-values). Let's use the first two points: (2, 10) and (3, 15).
Change in stretch = 15 - 10 = 5 mm
Change in weight = 3 - 2 = 1 g
Unit rate = Change in stretch / Change in weight = 5 mm / 1 g
Therefore, the unit rate is 5 millimeters per gram.