Concept explainers
Determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.
Whether the given function is linear or non linear. If linear, then find the equation of the line.
Answer to Problem 2CT
The equation of the given function is
Explanation of Solution
Given:
The given function is
Formula used:
A function is said to be linear if it has a constant slope.
That is, we have to check if the average rate of change of the function is constant.
The average rate of change is
The point-slope forms of the line through the point with slope is
Calculation:
The average rate of change of the given function is
Considering the first and the second points, we get
Considering the second and the third points, we get
Considering the third and the forth points, we get and so on.
Thus, we can see that the average rate of change of the given function is a constant.
Thus, the slope of the given function is
Now, we have to find the equation of the line.
Thus, let us use the point slope form of the line.
Let and the slope is
Thus, the equation of the line joining the above 2 points is
Thus, the equation of the given function is
Chapter 3 Solutions
Precalculus Enhanced with Graphing Utilities
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