To determine how much Dan makes per hour, we start by finding the unit rate.
Given:
- Dan makes [tex]$7.5$[/tex] dollars every [tex]$2.5$[/tex] hours.
1. Calculate the Unit Rate:
To find the unit rate (dollars per hour), we divide the total dollars earned by the total hours worked.
[tex]\[
\text{Unit rate} = \frac{7.5 \, \text{dollars}}{2.5 \, \text{hours}} = 3 \, \text{dollars per hour}
\][/tex]
This means Dan earns [tex]$3$[/tex] per hour.
2. Fill in the Ratio Table:
Next, we use the unit rate to fill in the table for different values of \( x \) (hours). Let's consider \( x \) values of \( 1 \) hour, \( 2 \) hours, and \( 3 \) hours.
[tex]\[
y = x \times 3
\][/tex]
Calculate \( y \) values:
- For \( x = 1 \) hour:
[tex]\[
y = 1 \times 3 = 3 \, \text{dollars}
\][/tex]
- For \( x = 2 \) hours:
[tex]\[
y = 2 \times 3 = 6 \, \text{dollars}
\][/tex]
- For \( x = 3 \) hours:
[tex]\[
y = 3 \times 3 = 9 \, \text{dollars}
\][/tex]
Therefore, the completed ratio table is:
[tex]\[
\begin{tabular}{|l|l|l|l|}
\hline
[tex]$x \, (\text{hr})$[/tex] & 1 & 2 & 3 \\
\hline
[tex]$y \, (\$[/tex])$ & 3 & 6 & 9 \\
\hline
\end{tabular}
\][/tex]
3. Graph the Relationship:
To graph the relationship, we plot the points from the ratio table on a coordinate plane where the x-axis represents hours \( x \) and the y-axis represents dollars \( y \).
- Point (1, 3)
- Point (2, 6)
- Point (3, 9)
Each of these points will align on a straight line, indicating a linear relationship where the slope of the line represents the unit rate (3 dollars per hour).
Thus, we've determined the unit rate, filled in the ratio table, and described how to graph the relationship.
