Question

During class today, Jeffrey's teacher gives everyone time to write their short stories. Jeffrey is proud of his story and wants to email it to his grandparents. So, after school he goes to the computer lab to type it.
This table shows the relationship between the amount of time (in minutes) Jeffrey types in the computer lab, x, and the total number of words he types, y.
x (minutes) y (words)
3 198
4 264
8 528
9 594
According to the values in the table, do x and y have a proportional relationship?
yes
no
What is the constant of proportionality? Write your answer as a whole number or decimal.

Answer 1

To determine if \( x \) (time in minutes) and \( y \) (words typed) have a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for all pairs of \( x \) and \( y \).

Let's calculate the ratios for each pair:

1. For \( x = 3 \) and \( y = 198 \):
\[
\frac{y}{x} = \frac{198}{3} = 66
\]

2. For \( x = 4 \) and \( y = 264 \):
\[
\frac{y}{x} = \frac{264}{4} = 66
\]

3. For \( x = 8 \) and \( y = 528 \):
\[
\frac{y}{x} = \frac{528}{8} = 66
\]

4. For \( x = 9 \) and \( y = 594 \):
\[
\frac{y}{x} = \frac{594}{9} = 66
\]

Since the ratio \( \frac{y}{x} \) is constant at 66 for all pairs, we can conclude that \( x \) and \( y \) do have a proportional relationship.

**Answer: Yes**

The constant of proportionality is:

**Answer: 66**