Chapter 4.2, Problem 28E

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 28E

The data can be modelled by a linear equation and linear equation is $y=-3x+7$

Explanation of Solution

Given: Data is

x	-3	-1	1	3	5
y	16	10	4	-2	-8

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	-3	-1	1	3	5
y	16	10	4	-2	-8

Slopes are calculated as follows:

  $m_1=\frac{10-16}{-1-\left(-3\right)}=\frac{10-16}{-1+3}=\frac{-6}{2}=-3$

  $m_2=\frac{4-10}{1-\left(-1\right)}=\frac{4-10}{1+1}=\frac{-6}{2}=-3$

  $m_3=\frac{-2-4}{3-1}=\frac{-6}{2}=-3$

  $m_4=\frac{-8-\left(-2\right)}{5-3}=\frac{-8+6}{5-3}=\frac{-6}{2}=-3$

Since the slope is constant

Thus, the data can be modelled by a linear equation

Equation of function is found by finding the equation of line passing through $\left(1,4\right)$ and $\left(3,-2\right)$

Thus, equation of line is calculated as follows:

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

Substituting the values in above equation:

  $\begin{array}{l}y-4=-3\left(x-1\right)\\ y-4=-3x+3\\ y=-3x+7\end{array}$

Conclusion:

Hence, the data can be modelled by a linear equation and linear equation is $y=-3x+7$