Chapter 4.2, Problem 30E

To determine

To calculate: To tell whether the data in the table can be modelled by a linear equation and if yes, then write the linear equation that represents $y$ as a function of $x$

Answer to Problem 30E

The data cannot be modelled by a linear equation

Explanation of Solution

Given: Data is

x	y
1	18
2	15
4	12
8	9

Formula Used:

If the slope of line is constant, then the data can be modelled by a linear equation.

Also, equation of line passing through two points is given as

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Data is given as follows:

x	y
1	18
2	15
4	12
8	9

Slopes are calculated as follows:

  $m_1=\frac{15-18}{2-1}=\frac{-3}{1}=-3$

  $m_2=\frac{12-15}{4-2}=\frac{-3}{2}=-\frac{3}{2}$

Since the slope is not constant

Thus, the data cannot be modelled by a linear equation

Conclusion:

Hence, the data cannot be modelled by a linear equation