The accompanying line graph shows how the average salary for baseball players in a certain league has increased over a​ 12-year period. Notice the average salary is given for​ odd-numbered years only. Also note that the left scale does not start at zero. Which​ 2-year period(s) had the smallest​ increase?

1 answer

To determine which 2-year periods had the smallest increase in the average salary for baseball players, you'll need to examine the specific data points provided by the line graph. Since the data points are given for odd-numbered years only, you will analyze the salary increments between these years (e.g., from Year 1 to Year 3, Year 3 to Year 5, etc.).

Here is a step-by-step approach you can follow:

1. **Identify Data Points:**
- Extract the salary values for each of the odd-numbered years depicted on the graph. For instance:
- Year 1: Salary \( S1 \)
- Year 3: Salary \( S3 \)
- Year 5: Salary \( S5 \)
- ... and so on until the final year presented.

2. **Calculate 2-Year Increases:**
- For each period, compute the increase in salary by subtracting the previous period's salary from the current period's salary.
- From Year 1 to Year 3: Increase \( I1 = S3 - S1 \)
- From Year 3 to Year 5: Increase \( I2 = S5 - S3 \)
- ... and continue this calculation up to the last data point available.

3. **Determine the Smallest Increase:**
- Compare the calculated increases (\( I1, I2, I3, \ldots \)) and identify which one is the smallest.

4. **Conclusion:**
- Note down the specific 2-year period(s) corresponding to the smallest increase.

It's difficult to pinpoint the exact values without the actual graph data, but with this method you can systematically determine which periods had the smallest increase in average salary by examining the calculated increments.

For illustration, if you found that the smallest increase is \( I3 \), corresponding to the period from Year 5 to Year 7, then you would conclude that the 2-year period from Year 5 to Year 7 had the smallest increase in average salary.

Without the actual numerical data from the graph, this description outlines the process you would follow. The key is to accurately extract the salary data points and perform simple subtractions to find the differences across each 2-year span.