Concept explainers
To find: the rate of change and determine whether a proportional linear relationship exists or not.
Answer to Problem 8PT
The linear relationship is proportional
The rate of change for the linear function is 2 steps stones per meter
Explanation of Solution
Given:
Calculation:
Consider three points from the graph that shows relationship between number of stepping stones and length of path:
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 number of stepping stones with respect to change in length of path.
So, consider two points as:
Thus, constant rate of change is:
Hence, rate of change for the linear function is 2 steps stones per meter
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
And. for the point
And also, for the point
Hence, ratio
Conclusion:
Thus, the linear relationship is proportional and the rate of change for the linear function is 2 steps stones per meter
Chapter 8 Solutions
Pre-Algebra, Student Edition
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