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

Answer 1

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

Let's calculate the ratios:

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

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

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

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

Since the ratio \( \frac{y}{x} = 66 \) is the same for all pairs, \( x \) and \( y \) have a proportional relationship.

Therefore, the answer is **yes**.