Concept explainers
To find: the constant rate of change and determine whether a proportional linear relationship exists between the two quantities.
Answer to Problem 6PPS
Hence, rate of change is 5lb/number of 1 iron weights. The linear relationship is proportional.
Explanation of Solution
Given:
Consider three points from the graph that shows relationship between iron weights and total weights: (2,10),(4,20) and (6,30)
Calculation:
In order to find constant rate of change, take any two points and use the formula for rate of change.
It means rate of change is change in total weights with respect to change in number of iron weights.
So, consider two points as: (2,10), (4,20)
Thus, constant rate of change is:
Hence, rate of change is 5lb/number of 1 iron weights.
Linear relationships are called proportional if the ration of each non- zeroy -value compared to corresponding x -value is the same.
Now, it means that calculate ratio
For the point (2,10) the ratio is:
And, for the point (4,20) the ratio is:
And also, for the point (6,30) the ratio is:
Hence, ratio
Thus, the linear relationship is proportional.
Conclusion:
Therefore, rate of change is 5lb/number of 1 iron weights. The linear relationship is proportional.
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