Question

Jake's grandparents get him a puppy for his thirteenth birthday, and he names the puppy Ruby. Jake does a good job taking care of Ruby, and she's growing so fast!
This table shows the relationship between Ruby's age (in months), x, and her weight (in pounds), y.
x (months) y (pounds)
2 6.5
4 12
6 17.5
10 28.5
According to the values in the table, do x and y have a proportional relationship?
yes
no

Answer 1

To determine if there is a proportional relationship between Ruby's age (x) and her weight (y), we need to check if the ratio of \( y \) to \( x \) (weight to age) is constant for all the given values.

Calculating the ratios:

1. For \( x = 2 \):
\[
\frac{y}{x} = \frac{6.5}{2} = 3.25
\]

2. For \( x = 4 \):
\[
\frac{y}{x} = \frac{12}{4} = 3
\]

3. For \( x = 6 \):
\[
\frac{y}{x} = \frac{17.5}{6} \approx 2.917
\]

4. For \( x = 10 \):
\[
\frac{y}{x} = \frac{28.5}{10} = 2.85
\]

The ratios are:
- \( \frac{6.5}{2} = 3.25 \)
- \( \frac{12}{4} = 3 \)
- \( \frac{17.5}{6} \approx 2.917 \)
- \( \frac{28.5}{10} = 2.85 \)

Since the ratios are not constant, we can conclude that \( x \) and \( y \) do not have a proportional relationship.

So the answer is **no**.