Question

annies 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. there is a proportional relationship between the age of annies 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

Explanation:

Step1: Recall proportional - relationship formula

For a proportional relationship $y = kx$, where $k$ is the constant of proportionality. We can find $k$ using the formula $k=\frac{y}{x}$.

Step2: Choose a data - point

Let's take the first data - point $(x = 4,y = 4)$.

Step3: Calculate the constant of proportionality

Substitute $x = 4$ and $y = 4$ into the formula $k=\frac{y}{x}$. So, $k=\frac{4}{4}=1$.
We can check with other data - points. For $(x = 21,y = 21)$, $k=\frac{21}{21}=1$; for $(x = 22,y = 22)$, $k=\frac{22}{22}=1$; for $(x = 27,y = 27)$, $k=\frac{27}{27}=1$.

Answer:

1