Over the summer, Springtown Science Academy renovates its building. The academy's principal hires Greta to lay new tile in the main hallway.

Question

This table shows the relationship between the length (in feet) of hallway Greta covers with tiles, x, and the number of tiles she needs, y.
x (feet) y (tiles)
2.5 30
3.5 42
6 72
7 84
According to the values in the table, do x and y have a proportional relationship?
yes
no

Answer 1

To determine if \( x \) (the length of hallway in feet) and \( y \) (the number of tiles) have a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for all the given pairs of values.

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

1. For \( x = 2.5 \) and \( y = 30 \): \[ \frac{y}{x} = \frac{30}{2.5} = 12 \]

2. For \( x = 3.5 \) and \( y = 42 \): \[ \frac{y}{x} = \frac{42}{3.5} = 12 \]

3. For \( x = 6 \) and \( y = 72 \): \[ \frac{y}{x} = \frac{72}{6} = 12 \]

4. For \( x = 7 \) and \( y = 84 \): \[ \frac{y}{x} = \frac{84}{7} = 12 \]

Since the ratio \( \frac{y}{x} \) is the same (12) for all the pairs, \( x \) and \( y \) do have a proportional relationship.

Answer: yes