Chapter 4.2, Problem 28E

To determine

To calculate: The data in the table can be modeled by a linear equation. Explain. If possible, write a linear equation that represent $y$ as a function of $x$ .

Answer to Problem 28E

The linear model is $y=-3x+7$ .

Explanation of Solution

Given information: The data in the table is:

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

Calculation: Firstly find the rate of change for consecutive data pair in the table.

  $\begin{array}{l}\frac{10-16}{-1+3}=\frac{-6}{2}=-3\\ \frac{4-10}{1+1}=\frac{-6}{2}=-3\\ \frac{-2-4}{3-1}=\frac{-6}{2}=-3\\ \frac{-8+2}{5-3}=\frac{-6}{2}=-3\end{array}$

Because the rate of change is constant, the data is linear. So use the point slope form to write an equation that represents the data.

Use the constant rate of change $\mathrm{slope}(m)=-3$ and the data to write an equation.

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-16=-3(x+3)\\ y-16=-3x-9\\ y=-3x-9+16\\ y=-3x+7\end{array}$

Thus the linear model is $y=-3x+7$ .