Question

does the table of values represent a proportional relationship? if so, state the constant of proportionality as a percent. if not, why?
x | 1.3 | 1.5 | 3
y | 1.56 | 1.8 | 3.6

Explanation:

Step1: Calculate $\frac{y}{x}$ for first pair

$\frac{1.56}{1.3} = 1.2$

Step2: Calculate $\frac{y}{x}$ for second pair

$\frac{1.8}{1.5} = 1.2$

Step3: Calculate $\frac{y}{x}$ for third pair

$\frac{3.6}{3} = 1.2$

Step4: Check for constant ratio

All $\frac{y}{x}$ ratios equal 1.2.

Answer:

Yes, the table represents a proportional relationship. The constant of proportionality is 120% (or 1.2 as a decimal, 120% as a percent). This is because the ratio $\frac{y}{x}$ is identical for all pairs of values in the table.