Use the image to answer the question.
A graph with an x-axis representing weight in grams ranges from 0 to 10 in unit increments and a y-axis representing length of stretch in millimeters ranges from 0 to 50 in increments of 5. A line passes through the following plotted points: left parenthesis 2 comma 10 right parenthesis; left parenthesis 3 comma 15 right parenthesis; and left parenthesis 7 comma 35 right parenthesis.
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.
(1 point)
mm per gram
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To find the unit rate, we need to determine how many millimeters the spring stretches for each gram of weight added. We can do this by finding the change in stretch (in millimeters) divided by the change in weight (in grams) between any two points on the line.
Let's take the points (2, 10) and (3, 15) on the line. The change in stretch is 15 - 10 = 5 millimeters, and the change in weight is 3 - 2 = 1 gram. Therefore, the unit rate is 5 millimeters per 1 gram.
We can also check this using the other set of points (3, 15) and (7, 35). The change in stretch is 35 - 15 = 20 millimeters, and the change in weight is 7 - 3 = 4 grams. The unit rate is 20 millimeters per 4 grams, which simplifies to 5 millimeters per 1 gram.
Therefore, the unit rate is 5 millimeters per gram.
To find the unit rate, we need to determine the amount of stretch in millimeters per gram of weight.
First, let's calculate the change in stretch (vertical change, y-axis) and the change in weight (horizontal change, x-axis) between each pair of plotted points.
From (2, 10) to (3, 15), the change in stretch is 15 - 10 = 5 millimeters, and the change in weight is 3 - 2 = 1 gram.
From (3, 15) to (7, 35), the change in stretch is 35 - 15 = 20 millimeters, and the change in weight is 7 - 3 = 4 grams.
Next, we need to find the ratio of the change in stretch to the change in weight for each pair of points.
For the first pair: 5 millimeters of stretch / 1 gram of weight = 5 millimeters/gram.
For the second pair: 20 millimeters of stretch / 4 grams of weight = 5 millimeters/gram.
Since the ratio of the change in stretch to the change in weight is the same for both pairs, we can conclude that the unit rate is 5 millimeters/gram.
Therefore, the unit rate for the stretch of the spring in millimeters is 5 millimeters per gram.
To find the unit rate, we need to determine the change in stretch per change in weight.
Looking at the plotted points, we can see that the weight increases by 1 gram from (2,10) to (3,15), and the stretch increases by 5 millimeters.
Therefore, the unit rate is:
5 millimeters / 1 gram
So, the unit rate is mm per gram.