Use 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 left parenthesis 2 comma 10 right parenthesis, left parenthesis 3 comma 15 right parenthesis, and left parenthesis 6 comma 30 right parenthesis. 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.
(1 point)
mm per gram
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The unit rate in this situation is the stretch of the spring in millimeters per gram of weight attached.
no, how many per gram
In this case, the unit rate is the number of millimeters of stretch per gram of weight attached.
And what is that number?
To determine the number of millimeters of stretch per gram of weight attached, we can use the points on the graph.
From the graph, we can see that when 2 grams of weight are attached, the spring stretches by 10 millimeters. When 3 grams of weight are attached, the spring stretches by 15 millimeters. And when 6 grams of weight are attached, the spring stretches by 30 millimeters.
To find the unit rate, we can calculate the change in stretch (in millimeters) divided by the change in weight (in grams).
Using the points (2, 10) and (3, 15), the change in stretch is 15 - 10 = 5 millimeters, and the change in weight is 3 - 2 = 1 gram.
So, the unit rate is 5 millimeters per 1 gram.
Therefore, the number of millimeters of stretch per gram of weight attached is 5.
Use the image to answer the question.
A line passes through the following plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 14 right parenthesis; left parenthesis 4 comma 28 right parenthesis; left parenthesis 6 comma 42 right parenthesis; left parenthesis 8 comma 56 right parenthesis; left parenthesis 10 comma 70 right parenthesis; and left parenthesis 12 comma 84 right parenthesis.
Using the points shown in the graph, identify the constant of proportionality for this graph.
(1 point)
$$
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To identify the constant of proportionality for this graph, we can examine the relationship between the x-values (weights) and the y-values (stretches).
From the graph, we can observe that as the weight (x-value) increases by 2 grams, the stretch (y-value) increases by 14 millimeters.
So, for every 2 gram increase in weight, there is a 14 millimeter increase in stretch.
Therefore, the constant of proportionality for this graph is 14 millimeters per 2 grams.
No. k equals what?
I apologize for the confusion. To determine the constant of proportionality, we need to calculate the ratio of the change in the y-values (stretches) to the corresponding change in the x-values (weights).
Looking at the graph, we can see that as the weight (x-value) increases by 2 grams, the stretch (y-value) increases by 14 millimeters.
So, the change in stretch is 14 millimeters and the corresponding change in weight is 2 grams.
To find the constant of proportionality (k), we divide the change in stretch by the change in weight:
k = change in stretch / change in weight
k = 14 millimeters / 2 grams
k = 7 millimeters per gram
Therefore, the constant of proportionality for this graph is 7 millimeters per gram.