Chapter 3.2, Problem 11E

To determine

To calculate: To determine whether the table represents a linear or non-linear function

Answer to Problem 11E

Graph represents linear function

Explanation of Solution

Given: Table is

x	1	2	3	4
y	5	10	15	20

Formula Used:

Linear functions are polynomials with degree of $1$ and have constant slopes. Graph of linear function is a straight line

Non-linear functions are polynomials with degree of more than $1$ and have a slope that varies between points. Graph of non-linear function is a curved line

Calculation:

Table is

x	1	2	3	4
y	5	10	15	20

Calculate the slope for the above:

  $m_1=\frac{10-5}{2-1}=\frac{5}{1}=5$

  $m_2=\frac{15-10}{3-2}=\frac{5}{1}=5$

  $m_3=\frac{20-15}{4-3}=\frac{5}{1}=5$

Since the slope is constant, thus it’s a linear function

Conclusion:

Hence, graph represents linear function