Chapter 9.7, Problem 18PPE

To determine

To find the best function that models the data and write its equation.

Answer to Problem 18PPE

The linear function $y=59x+189$ best models the data.

Explanation of Solution

Given information:

The number of people attending a school’s first five football games is shown in the table below:

  

Graph the data:

  

The graph seems to a straight line. It may be a linear function.

Test for common differences:

The y-values have a common difference of $59$ . A linear model fits the data.

Write a linear model:

The linear model is given by $y=mx+c$

Here, $m=\frac{y_2-y_1}{x_2-x_1}$ is the slope and $c$ is the y-intercept of the line.

  $\begin{array}{c}m=\frac{307-248}{2-1}\\ =59\end{array}$

Thus, the model is $y=59x+c$ .

Find the value of $c$ .

The line passes through $\left(1,248\right)$

Therefore,

  $\begin{array}{c}248=59\left(1\right)+c\\ c=248-59\\ =189\end{array}$

Hence, the linear model is given by $y=59x+189$ .