Chapter 1.3, Problem 18E

To determine

To write: The equation of a line of fit for the data. Also find the number of tickets sold when the ticket price is $85.

Answer to Problem 18E

The equation of line is $y=\frac{-55x}{9}+\frac{4985}{9}$

When $x=85$ then $y=34.44$

Explanation of Solution

Given Information: The table is given as:

Tickets price (dollars), x	17	20	22	26
Tickets sold, y	450	423	400	395

The graph by taking points (17,450), (20,423), (22,400), (26,395) on graph. It shows a linear graph.

Now find the slope of line by taking any two points (26, 395) and (17, 450).

Slope $=\frac{y_2-y_1}{x_2-x_1}$

  $=\frac{450-395}{17-26}$

  $=\frac{55}{-9}=\frac{-55}{9}$

Now equation of line using point slope from

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-395=\frac{-55}{9}(x-26)\end{array}$

  $\begin{array}{l}y-395=\frac{-55x}{9}+\frac{1430}{9}\\ y=\frac{-55x}{9}+\frac{1430}{9}+395\\ y=\frac{-55x}{9}+\frac{4985}{9}\end{array}$

Now put $x=\text{ 8}5$

  $\begin{array}{l}y=\frac{-55}{9}(85)+\frac{4985}{9}\\ y=\frac{-4675}{9}+\frac{4985}{9}\\ y=\frac{310}{9}\\ y=34.44\end{array}$

This show that price is reasonable because relationship is linear.