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The tree's average monthly increase in height during the first 4 months was 6 1/4 inches.

To determine the average monthly increase in height of the tree over the first four months, we need to calculate the total height increase and then divide it by the number of months. The tree started at 8 inches and reached a height that allows us to find that average.

A) 5 1/4 in

This option suggests that the tree increased in height by 5 1/4 inches on average. However, calculating the total increase using this average would not yield a final height consistent with the graph data, making this option incorrect.

B) 6 1/4 in

This is the correct option, indicating that the tree had an average height increase of 6 1/4 inches per month. This average, when multiplied by 4 months, aligns with the total increase observed in the graph, confirming its accuracy.

C) 6 3/4 in

While this option presents a significant height increase, it suggests an average that, when calculated over 4 months, would result in a total increase that does not match the observed data. Therefore, this option is incorrect.

D) 7 1/4 in

This option implies a relatively high average increase in height. However, if the tree had grown at this rate, it would have surpassed the height indicated in the graph, making this option inconsistent with the information provided.

E) 7 3/4 in

This choice indicates an even higher average monthly increase. Similar to option D, it would lead to a final height that exceeds the observed height from the graph, thereby rendering this option incorrect.

Conclusion

The average monthly increase of 6 1/4 inches is the only option that accurately reflects the tree's growth over the specified period, as supported by the graph data. All other options either underestimate or overestimate the increase, failing to align with the observed final height of the tree after four months.