Question

brittanys favorite book is about johnny appleseed, the american pioneer who planted apple trees all across the country. inspired by the story, brittany plants an apple seed in her backyard and tends the seed as it slowly grows into a tree. this table shows the relationship between the age of brittanys apple tree (in years), x, and the height of the tree (in feet), y. according to the values in the table, do x and y have a proportional relationship? yes no

Explanation:

Step1: Recall the definition of proportional relationship

For a proportional relationship \(y = kx\), where \(k\) is the constant of proportionality. So, \(\frac{y}{x}=k\) (constant) for all pairs \((x,y)\).

Step2: Calculate \(\frac{y}{x}\) for each pair

For the first pair \((x = 3,y = 3)\): \(\frac{y}{x}=\frac{3}{3}=1\).
For the second pair \((x = 7,y = 7)\): \(\frac{y}{x}=\frac{7}{7}=1\).
For the third pair \((x = 26,y = 26)\): \(\frac{y}{x}=\frac{26}{26}=1\).
For the fourth pair \((x = 28,y = 28)\): \(\frac{y}{x}=\frac{28}{28}=1\).

Since \(\frac{y}{x}=1\) (constant) for all pairs of \(x\) and \(y\) values in the table.

Answer:

Yes