Chapter 5.4, Problem 23P

A sign says that 3 tickets cost $ 22.50 and that 7 tickets cost $ 52.50. Write an equation in point-slope form that represents the cost of tickets. What is the graph of the equation?

To determine

To Write: An equation in point-slope form that represents the cost of the tickets. Also, graph the equation.

Answer to Problem 23P

  $y-22.50=7.5(x-3)$

Explanation of Solution

Given information: 3 tickets cost $22.50 and that 7 ticket cost $52.50.

Formula used: Point-slope form is $y-y_1=m(x-x_1)$ Where m is slope and $(x_1,y_1)$ is a point. Formula to find $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

From given information make two points as (3, 22.50) and (7,52.50)

Find slope of the line using the formula

  $m=\frac{52.50-22.50}{7-3}$

Simplify it,

  $=\frac{30}{4}$

  $m=7.5$

Now, use any of the given points and slope as 7.5 into the formula $y-y_1=m(x-x_1)$

Here, use (3,22.50) as a point to get equation as

  $y-22.50=7.5(x-3)$

Point-slope form of a line is $y-22.50=7.5(x-3)$

Represent the point (3,22.50) and the another point (7,52.50) on the xy plane then join them and extend the line on both ends.

  

The graph starts at (0,0) because in real life situation the number of tickets purchased cannot be a negative number. So, the graph lies in first quadrant and passes through (0,0) and (7,52.5).