Using the points shown in the graph, identify the constant of proportionality for this graph length of stretch (mm)
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14-
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To find the constant of proportionality for this graph, we can calculate the ratio of the change in the length of stretch (mm) to the corresponding change in the input value (X).
From the graph, we can see that the length of stretch decreases by 14 mm for every 2 units increase in X.
So, the constant of proportionality is 14 mm/2 = 7 mm per unit.
To identify the constant of proportionality for the graph, you need to find the ratio between the change in the length of stretch and the change in the x-values.
In this case, the length of stretch (mm) is plotted on the y-axis (vertical axis), while the x-values are plotted on the x-axis (horizontal axis).
Take two points on the graph, for example, (2, 70) and (4, 56). The change in the length of stretch is 70 - 56 = 14 mm, and the change in x-values is 4 - 2 = 2.
To find the constant of proportionality, divide the change in the length of stretch by the change in x-values:
Constant of proportionality = (Change in length of stretch) / (Change in x-values)
Constant of proportionality = 14 mm / 2 = 7 mm
Therefore, the constant of proportionality for this graph is 7 mm.
To identify the constant of proportionality for the graph, we need to determine the ratio of the length of stretch (mm) to the corresponding values of x.
Let's calculate the ratios for two points on the graph:
- Point 1: (x=4, length of stretch = 56 mm)
- Point 2: (x=6, length of stretch = 42 mm)
The ratio for Point 1 is: 56 mm / 4 = 14 mm/x
The ratio for Point 2 is: 42 mm / 6 = 7 mm/x
Since we want to find the constant of proportionality, the ratios should be equal. So, we can set up the equation:
14 mm/x = 7 mm/x
Now, we can solve for x by cross-multiplying:
14 mm * x = 7 mm * x
Simplifying the equation, we get:
14x = 7x
Subtracting 7x from both sides, we get:
7x = 0
Dividing both sides by 7, we find:
x = 0
Therefore, the constant of proportionality for this graph is x = 0.