Concept explainers
To find: the constant rate of change and determine whether a proportional linear relationship exists between the two quantities.
Answer to Problem 1CYU
Rate of change is
The linear relationship is not proportional.
Explanation of Solution
Given:
Consider three points from the graph that shows relationship between number of weeks and height of plants in inches: (0,3),(2,4) and (6,6)
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 height of plants with respect to change in number of weeks.
So, consider two points as: (0,3),(2,4)
Thus, constant rate of change is:
Hence, rate of change is
Linear relationships are called proportional if the ration of each non zero y-value compared to corresponding x-value is the same.
Now, it means that calculate ratio
For the point (0,3) the ratio is:
And, for the point (2,4) the ratio is:
And also, for the point (6,6) the ratio is:
Hence, ratio
Thus, the linear relationship is not proportional
Conclusion:
Therefore, rate of change is
The linear relationship is not proportional.
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