Final answer:
Using the line of best fit equation y = 9/2x + 22, if x is 2 (representing age in years), the average height (y) is 31 inches, indicating children will be on average 31 inches taller at 2 years old.
Step-by-step explanation:
The equation of the line of best fit given is y = \frac{9}{2}x + 22. To find out how many inches taller children will grow on average when they are 2 years old, we need to substitute x with 2 in the equation (since x represents the age in years). Therefore, y will be:
y = \frac {9}{2}(2) + 22
y = 9 + 22
y = 31
So, on average, children will grow about 31 inches taller when they are 2 years old, which corresponds to answer option d.