Chapter 11.8, Problem 56SR

To determine

the model which fits the given data

Answer to Problem 56SR

The table of values represents a linear equation.

Explanation of Solution

Given:

x	3	4	5	6	7
y	3	5	7	9	11

Calculation:

The table of values is as follows.

x	3	4	5	6	7
y	3	5	7	9	11

The objective is to determine the model which fits the above data. And then write the equation for the function that models the data.

At first find the differences of the data of the $y$ values.

So,

  $\begin{array}{l}5-3=2\hfill \\ 7-5=2\hfill \\ 9-7=2\hfill \\ 11-9=2\hfill \end{array}$

The first differences are all equal. So, the table of values represents a linear equation.

Now, the constant value is calculated below.

  $\begin{array}{l}y=mx+b\hfill \\ 3=2\left(3\right)+b\hfill \\ 3=6+b\hfill \\ \frac{1}{2}=b\hfill \end{array}$

Therefore, the equation is $y=2x+\frac{1}{2}$ .

Conclusion:

The table of values represents a linear equation.