Question

luke owns and operates stain - b - gone carpet cleaners. he uses a special non - toxic cleaning solution to clean carpets. this table shows the relationship between the amount of cleaning solution (in quarts) luke uses, x, and the area of carpet (in square yards) he cleans with the solution, y.

x (quarts)	y (square yards)
7	70
8	80
9	90

according to the values in the table, do x and y have a proportional relationship?
yes
no

Explanation:

Step1: Calculate the ratio for each pair

For the first pair: $\frac{y}{x}=\frac{20}{2} = 10$.
For the second pair: $\frac{y}{x}=\frac{70}{7}=10$.
For the third pair: $\frac{y}{x}=\frac{80}{8}=10$.
For the fourth pair: $\frac{y}{x}=\frac{90}{9}=10$.

Step2: Check if ratios are equal

Since the ratio $\frac{y}{x}$ is equal to 10 for all pairs of values in the table.

Answer:

yes