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X -1 3 7 11 15 y -9 -4 1 6 11 a. Is it a linear function? b. Why/Why not?

X -1 3 7 11 15 y -9 -4 1 6 11 a. Is it a linear function? b. Why/Why not?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 35E
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### Problem 4 #### Data Table The table contains pairs of x and y values: | x | y | |----|----| | -1 | -9 | | 3 | -4 | | 7 | 1 | | 11 | 6 | | 15 | 11 | #### Questions: a. Is it a linear function? b. Why/Why not? **Explanation:** To determine if the data represents a linear function, check if the change in y-values is consistent with the change in x-values across the table. 1. Calculate the differences between consecutive x-values: - \(3 - (-1) = 4\) - \(7 - 3 = 4\) - \(11 - 7 = 4\) - \(15 - 11 = 4\) Here, the change in x is consistently 4. 2. Calculate the differences between consecutive y-values: - \(-4 - (-9) = 5\) - \(1 - (-4) = 5\) - \(6 - 1 = 5\) - \(11 - 6 = 5\) Here, the change in y is consistently 5. Since the rate of change between x and y is consistent, the relationship is linear. The slope of the function, derived from these changes, is \(\frac{5}{4}\).
Transcribed Image Text:### Problem 4 #### Data Table The table contains pairs of x and y values: | x | y | |----|----| | -1 | -9 | | 3 | -4 | | 7 | 1 | | 11 | 6 | | 15 | 11 | #### Questions: a. Is it a linear function? b. Why/Why not? **Explanation:** To determine if the data represents a linear function, check if the change in y-values is consistent with the change in x-values across the table. 1. Calculate the differences between consecutive x-values: - \(3 - (-1) = 4\) - \(7 - 3 = 4\) - \(11 - 7 = 4\) - \(15 - 11 = 4\) Here, the change in x is consistently 4. 2. Calculate the differences between consecutive y-values: - \(-4 - (-9) = 5\) - \(1 - (-4) = 5\) - \(6 - 1 = 5\) - \(11 - 6 = 5\) Here, the change in y is consistently 5. Since the rate of change between x and y is consistent, the relationship is linear. The slope of the function, derived from these changes, is \(\frac{5}{4}\).
Expert Solution
Step 1: About linear function

We know the slope of linear function is constant.

Slope=fraction numerator c h a n g e space i n space y space v a l u e s over denominator c h a n g e space i n space x space v a l u e s end fraction.


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