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 20 35 54 77 y 5 7 9 11 ∘ proportional y is \\(\square\\) times x ∘ not proportional table 2 x 10 14 18 22 y 15 21 27 33 ∘ proportional y is \\(\square\\) times x ∘ not proportional

Explanation:

Step1: Check Table 1 ratios

Calculate $\frac{y}{x}$ for each pair:
$\frac{5}{20}=\frac{1}{4}$, $\frac{7}{35}=\frac{1}{5}$, $\frac{9}{54}=\frac{1}{6}$, $\frac{11}{77}=\frac{1}{7}$

Step2: Evaluate Table 1 proportionality

Ratios are not equal, so not proportional.

Step3: Check Table 2 ratios

Calculate $\frac{y}{x}$ for each pair:
$\frac{15}{10}=\frac{3}{2}$, $\frac{21}{14}=\frac{3}{2}$, $\frac{27}{18}=\frac{3}{2}$, $\frac{33}{22}=\frac{3}{2}$

Step4: Evaluate Table 2 proportionality

All ratios are equal, so proportional with $y=\frac{3}{2}x$.

Answer:

Table 1: Not proportional
Table 2: Proportional, $y$ is $\frac{3}{2}$ times $x$