Question

for each table, determine whether it shows that x and y are proportional. if x and y are proportional, fill in the blank with a number in simplest form. table 1 x 6 9 12 y 12 36 72 proportional y is box times x not proportional table 2 x 6 8 10 y 24 32 40 proportional y is box times x not proportional

Explanation:

Step1: Check Table 1 ratios

Calculate $\frac{y}{x}$ for each pair:
$\frac{12}{6}=2$, $\frac{36}{9}=4$, $\frac{72}{12}=6$

Step2: Evaluate Table 1 proportionality

Ratios are not equal, so not proportional.

Step3: Check Table 2 ratios

Calculate $\frac{y}{x}$ for each pair:
$\frac{24}{6}=4$, $\frac{32}{8}=4$, $\frac{40}{10}=4$

Step4: Evaluate Table 2 proportionality

All ratios equal 4, so $y=4x$.

Answer:

Table 1: Not proportional
Table 2: Proportional, $y$ is $4$ times $x$