Question

example
the table shows the costs for different numbers of tickets for the band concert. find the unit cost.
use a table
the ratios in the table are all equivalent, so you can divide the cost by the number of tickets in any of the ratios to find the unit cost.
$\frac{\\$24}{4 \text{ tickets}}=\frac{\\$6}{1 \text{ ticket}}$ or $\\$6$ for 1 ticket
the unit cost is $6$.
use a graph
the graph of the data shows that the cost of one ticket, is $\\$6$, so the unit cost is $6$.
1 explain what the unit cost means in the context of the example problem.
2 use two points on the graph to find the slope. how does the slope relate to the unit cost?
3 use the slope you found in problem 2 to write an equation for finding the cost $y$ of $x$ tickets.

Explanation:

Step1: Understand Unit Cost Concept

Unit cost is the cost per one unit (here, per one ticket). In the context of the band - concert tickets, it means the amount of money needed to buy one ticket.

Step2: Calculate Slope Using Points

Let's take two points from the graph, say \((1,6)\) and \((2,12)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 1,y_1=6,x_2 = 2,y_2 = 12\) into the formula:
\(m=\frac{12 - 6}{2 - 1}=\frac{6}{1}=6\)
The slope represents the rate of change. In this case, for each additional ticket (\(x\) increases by 1), the cost (\(y\)) increases by 6. So the slope is equal to the unit cost.

Step3: Write the Equation

The slope - intercept form of a line is \(y=mx + b\). Since the line passes through the origin \((0,0)\) (when \(x = 0\) tickets, \(y=0\) cost), \(b = 0\).
Using \(m = 6\) (from step 2), the equation is \(y=6x\)

Answer:

1. The unit cost means the cost of one band - concert ticket.
2. Using points \((1,6)\) and \((2,12)\), slope \(m=\frac{12 - 6}{2 - 1}=6\). The slope is equal to the unit cost as it shows the increase in cost per one additional ticket.
3. The equation is \(y = 6x\)