Question

As a math teacher, Josie frequently makes photocopies of fun activities for her students to do. When the copies come out of the copy machine, they form a stack.
This table shows the relationship between the number of copies in the stack, x, and the height (in millimeters) of the stack, y.
x (copies) y (millimeters)
20 2
50 5
60 6
70 7
According to the values in the table, do x and y have a proportional relationship?
yes
no

Answer 1

What is the constant of proportionality? Write your answer as a whole number or decimal.
millimeters per copy

Answer 2

To determine if \( x \) (number of copies) and \( y \) (height in millimeters) have a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for the values given in the table.

Let's calculate the ratio \( \frac{y}{x} \) for each pair of values:

1. For \( x = 20 \):
\[
\frac{y}{x} = \frac{2}{20} = \frac{1}{10} = 0.1
\]

2. For \( x = 50 \):
\[
\frac{y}{x} = \frac{5}{50} = \frac{1}{10} = 0.1
\]

3. For \( x = 60 \):
\[
\frac{y}{x} = \frac{6}{60} = \frac{1}{10} = 0.1
\]

4. For \( x = 70 \):
\[
\frac{y}{x} = \frac{7}{70} = \frac{1}{10} = 0.1
\]

Since the ratio \( \frac{y}{x} \) is the same (0.1) for all values of \( x \) and \( y \), we conclude that \( x \) and \( y \) do have a proportional relationship.

So the answer is:
**yes**.

Answer 3

The constant of proportionality \( k \) can be found from the ratios \( \frac{y}{x} \) that we previously calculated, which is the same for all pairs of values.

The constant of proportionality is:

\[
k = \frac{y}{x} = 0.1 \text{ millimeters per copy}
\]

Thus, the constant of proportionality is:

**0.1 millimeters per copy**.