Annie's favorite book is about Johnny Appleseed, the American pioneer who planted apple trees all across the country. Inspired by the story, Annie plants an apple seed in her backyard and tends the seed as it slowly grows into a tree.

Question

There is a proportional relationship between the age of Annie's apple tree (in years), x, and the height of the tree (in feet), y.
x (years) y (feet)
4 4
21 21
22 22
27 27
What is the constant of proportionality? Write your answer as a whole number or decimal.
feet per year

Answer 1

To find the constant of proportionality in the relationship between the age of Annie's apple tree (in years) \( x \) and the height of the tree (in feet) \( y \), we can divide the height \( y \) by the age \( x \) for any of the given points.

Let's use the first point \( (4, 4) \):

\[ \text{Constant of proportionality} = \frac{y}{x} = \frac{4}{4} = 1 \]

Now, let's check with the other points to ensure consistency:

• For the second point \( (21, 21) \): \[ \frac{21}{21} = 1 \]
• For the third point \( (22, 22) \): \[ \frac{22}{22} = 1 \]
• For the fourth point \( (27, 27) \): \[ \frac{27}{27} = 1 \]

Since all calculations give us the same ratio, the constant of proportionality is \( 1 \).

Therefore, the constant of proportionality is:

\[ \boxed{1} \text{ feet per year} \]