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Text Solution:

Since the height of the tree varies directly with its age in years, we can create a direct variation equation in which h = height of the tree, a = age of the tree, and k = some unknown constant, giving us h = ka. Since we are given that the height of the tree is 80 feet when the tree is 100 years old, we can substitute these values into the equation to determine k:

$\begin{array}{l}\Rightarrow h=ka\\ \Rightarrow 80=k\times 100\\ \Rightarrow \frac{80}{100}=k\\ \Rightarrow 0.8=k\end{array}$

We now know that our direct variation equation for this problem is h = 0.8a. In order to calculate the height of the tree when the tree was 9 years old, we can substitute 9 for a and find the value of h:

$\begin{array}{l}\Rightarrow h=0.8a\\ \Rightarrow h=0.8\times 9\\ \Rightarrow h=7.2\end{array}$

Thus, the height of the tree when the tree was 9 years old was 7.2 feet.