Question

While relaxing on his front porch, Larry notices a garden snail crawling on the sidewalk. Larry is amazed at how slowly the snail moves, so he starts timing it.
There is a proportional relationship between the amount of time (in minutes) that Larry spends timing the snail, x, and the distance (in feet) that the snail moves, y.
x (minutes) y (feet)
3 6
5 10
9 18
14 28
What is the constant of proportionality? Write your answer as a whole number or decimal.
feet per minute

Answer 1

To find the constant of proportionality (k) for the relationship between the time (x in minutes) and the distance (y in feet), we can use the formula for direct proportionality:

\[
y = kx
\]

We can use any of the pairs (x, y) given in the table. Let's use the pair (3, 6):

\[
6 = k \cdot 3
\]

Now, solve for k:

\[
k = \frac{6}{3} = 2
\]

So, the constant of proportionality is 2. This means the snail moves at a speed of 2 feet per minute.

We can double-check this with other pairs:

For the pair (5, 10):
\[
10 = k \cdot 5 \implies k = \frac{10}{5} = 2
\]

For the pair (9, 18):
\[
18 = k \cdot 9 \implies k = \frac{18}{9} = 2
\]

For the pair (14, 28):
\[
28 = k \cdot 14 \implies k = \frac{28}{14} = 2
\]

In each case, we consistently find that the constant of proportionality is \( k = 2 \).

Thus, the constant of proportionality is **2 feet per minute**.