Question
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)
Use the image to answer the question.
A graph shows an x-axis ranging from 0 to 12 in increments of 2 and a y-axis ranging from 0 to 84 in increments of 14. 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)
To find the unit rate, we need to determine the ratio of the change in the length of stretch to the change in weight for any given interval.
Using the points (2,10), (3,15), and (7,35), we can calculate the change in the length of stretch and the change in weight.
Change in length of stretch:
From (2,10) to (3,15): 15 - 10 = 5 mm
From (3,15) to (7,35): 35 - 15 = 20 mm
Change in weight:
From (2,10) to (3,15): 3 - 2 = 1 g
From (3,15) to (7,35): 7 - 3 = 4 g
Now, we can calculate the unit rate by dividing the change in length of stretch by the change in weight:
For the interval from (2,10) to (3,15) :
Unit rate = (Change in length of stretch) / (Change in weight) = 5 mm / 1 g = 5 mm/g
For the interval from (3,15) to (7,35) :
Unit rate = (Change in length of stretch) / (Change in weight) = 20 mm / 4 g = 5 mm/g
Therefore, the unit rate is 5 mm/g.
To find the constant of proportionality, we need to determine how the y-values (lengths) change in relation to the x-values (weights).
Looking at the given points, we can see that the y-values increase by 14 for every increase of 2 in the x-values.
For example:
- From (0, 0) to (2, 14), the y-value increases by 14 for a 2-unit increase in the x-value.
- From (2, 14) to (4, 28), the y-value again increases by 14 for a 2-unit increase in the x-value.
- This pattern continues for all the given points.
So, for every 2-unit increase in weight (x-value), the length of stretch (y-value) increases by 14.
Therefore, the constant of proportionality for this graph is 14.
The unit rate can be found by determining how much the length of the stretch increases for every gram increase in weight.
Using the given plotted points, we can calculate the change in length of the stretch for each gram increase in weight.
The change in length for the first point is 15-10 = 5 mm for a 1 gram increase in weight.
The change in length for the second point is 35-15 = 20 mm for a 4 gram increase in weight (7-3 = 4).
Since these changes are not the same, it means that the unit rate is not constant. Therefore, we cannot determine a single unit rate from the given points.