Chapter 1.7, Problem 12HP

To determine

The equation to find the total cost c for t tickets

Answer to Problem 12HP

The equation to find the total cost is $c=26t$

Explanation of Solution

Given information:

Tickets to an amusement park are $26 each

Concept Used:

  $\text{cost}c=26t$

The slope of a line connecting the points $\left(x_1,y_1\right),\text{ and }\left(x_2,y_2\right)$ is given by the formula

  $\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}\text{Equation}\text{is}\\ \text{y}-{\text{y}}_1=m\left(x-x_1\right)\end{array}$

Calculation:

The slope of the line passing through the points $\left(1,26\right),\text{ and }\left(2,52\right)$ , use the slope formula and substitute the values $\left(x_1,y_1\right)=\left(1,26\right),\text{ and }\left(x_2,y_2\right)=\left(2,52\right)$ and simplify further as shown below,

  $\begin{array}{c}\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{52-26}{2-1}\\ =26\end{array}$

  $\begin{array}{l}\text{Equation}\text{is}\\ \text{y}-{\text{y}}_1=m\left(x-x_1\right)\\ y-26=26\left(x-1\right)\\ y-26=26x-26\\ y-26+26=26x-26+26\\ y=26x\\ c=26t\end{array}$

Thus, the equation to find the total cost is $c=26t$

In order to find the table we put the value of t in this equation $\text{cost}c=26t$

  $\begin{array}{c}c=26t\\ t=1\\ c=26\cdot 1\\ =26\\ t=2\\ c=26\times 2\\ =52\\ t=3\\ c=26\times 3\\ =78\\ t=4\\ c=26\times 4\\ =104\end{array}$

The table is

Ticket t	Cost c
1	26
2	52
3	78
4	104