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	5	6	7	8
y	25	30	35	40

○ proportional
y is \\(\square\\) times x
○ not proportional
table 2

x	5	7	9	11
y	5	21	45	77

○ proportional
y is \\(\square\\) times x
○ not proportional

Explanation:

Step1: Check Table 1 ratios

Calculate $\frac{y}{x}$ for each pair:
$\frac{25}{5}=5$, $\frac{30}{6}=5$, $\frac{35}{7}=5$, $\frac{40}{8}=5$

Step2: Confirm Table 1 proportionality

All $\frac{y}{x}$ ratios equal 5, so $y=5x$.

Step3: Check Table 2 ratios

Calculate $\frac{y}{x}$ for each pair:
$\frac{5}{5}=1$, $\frac{21}{7}=3$, $\frac{45}{9}=5$, $\frac{77}{11}=7$

Step4: Confirm Table 2 non-proportionality

Ratios are not equal, so no constant multiplier.

Answer:

Table 1: Proportional, $y$ is 5 times $x$
Table 2: Not proportional