Question

In a flash of sheer brilliance, Colton invents a time machine! The machine uses a small nuclear reactor to generate the electricity it needs to travel back in time.
This table shows the relationship between how many years Colton wants to travel back in time, x, and how much electricity (in megawatts) his time machine needs, y.
x (years) y (megawatts)
13 312
14 336
18 432
35 840
According to the values in the table, do x and y have a proportional relationship?
yes
no

Answer 1

To determine whether the variables \( x \) (years) and \( y \) (megawatts) have a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for all pairs of values in the table.

Let's compute the ratio for each pair:

1. For \( x = 13 \) and \( y = 312 \):
\[
\frac{y}{x} = \frac{312}{13} = 24
\]

2. For \( x = 14 \) and \( y = 336 \):
\[
\frac{y}{x} = \frac{336}{14} = 24
\]

3. For \( x = 18 \) and \( y = 432 \):
\[
\frac{y}{x} = \frac{432}{18} = 24
\]

4. For \( x = 35 \) and \( y = 840 \):
\[
\frac{y}{x} = \frac{840}{35} = 24
\]

Since the ratio \( \frac{y}{x} \) is consistently 24 for all the pairs, \( x \) and \( y \) have a proportional relationship.

Therefore, the answer is **yes**.