To determine which employee earns more per hour, let’s analyze the earnings per hour for each based on the information from the graphs.

Step 1: Observing the Data Points

Both graphs show the earnings ($y$) over hours ($x$) for each employee, represented by a straight line, suggesting a constant hourly rate.

1. Employee 1:

   • At 2 hours: $30
   • At 4 hours: $50
   • At 6 hours: $80

2. Employee 2:

   • At 2 hours: $20
   • At 4 hours: $50
   • At 6 hours: $80

Step 2: Calculating Earnings per Hour (Hourly Rate)

The hourly rate can be found by dividing the change in earnings by the change in hours (slope of the line):

Employee 1:

• Change in earnings from 0 hours to 6 hours: $80 - 0 = 80$
• Change in time from 0 hours to 6 hours: $6 - 0 = 6$
• Hourly rate for Employee 1 = $\frac{80}{6} \approx 13.33$ dollars per hour.

Employee 2:

• Change in earnings from 0 hours to 6 hours: $80 - 0 = 80$
• Change in time from 0 hours to 6 hours: $6 - 0 = 6$
• Hourly rate for Employee 2 = $\frac{80}{6} \approx 13.33$ dollars per hour.

Conclusion

Both Employee 1 and Employee 2 have the same earnings rate of approximately $13.33 per hour. Thus, neither employee earns more per hour; their hourly rates are identical.

Would you like more details on how this was calculated or have any further questions?

Here are five additional related questions to deepen understanding:

1. How can we use slope calculations to determine hourly rates from a graph?
2. What would change if one employee had a higher initial earnings value?
3. How would the graph look if one employee worked fewer hours but earned the same total amount?
4. Can the hourly rate change if the line is curved instead of straight? Why or why not?
5. How does understanding slope in a real-world context, like wages, help with interpreting other types of data?

Tip: To find hourly rates from a graph, look for two clear points and divide the difference in earnings by the difference in time.