Chapter 3.2, Problem 26E

To determine

To calculate: To fill in the table so it represents a linear function

Answer to Problem 26E

Completed table is

x	5	10	15	20	25
y	-1	2	5	8	11

Explanation of Solution

Given: Table is

x	5	10	15	20	25
y	-1				11

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	5	10	15	20	25
y	-1				11

Slope of function is calculated as

  $m=\frac{25-5}{11+1}=\frac{20}{12}=\frac{5}{3}$

Calculate the slope for the above:

  $\begin{array}{l}{m}_1=\frac{10-5}{x+1}=\frac{5}{3}\\ \frac{5}{x_1+1}=\frac{5}{3}\\ \frac{1}{x_1+1}=\frac{1}{3}\\ x_1+1=3\\ x_1=2\end{array}$

Also,

  $\begin{array}{l}{m}_2=\frac{15-10}{x_2-2}=\frac{5}{3}\\ \frac{5}{x_2-2}=\frac{5}{3}\\ \frac{1}{x_2-2}=\frac{1}{3}\\ x_2-2=3\\ x_2=5\end{array}$

Also,

  $\begin{array}{l}{m}_2=\frac{20-15}{x_3-5}=\frac{5}{3}\\ \frac{5}{x_3-5}=\frac{5}{3}\\ \frac{1}{x_3-5}=\frac{1}{3}\\ x_3-5=3\\ x_3=8\end{array}$

Thus, completed table is as follows:

x	5	10	15	20	25
y	-1	2	5	8	11

Conclusion:

Hence, table is completed to represent a function