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: 4, 6, 8
y: 16, 48, 32
proportional
y is \\(\square\\) times x
not proportional
table 2
x: 5, 8, 11
y: 15, 24, 33
proportional
y is \\(\square\\) times x
not proportional

Explanation:

Step1: Check Table 1 for Proportionality

To check if \( x \) and \( y \) are proportional, we verify if \( \frac{y}{x} \) is constant for all pairs.
For \( x = 4, y = 16 \): \( \frac{16}{4} = 4 \)
For \( x = 6, y = 48 \): \( \frac{48}{6} = 8 \)
For \( x = 8, y = 32 \): \( \frac{32}{8} = 4 \)
Since \( \frac{y}{x} \) is not constant (4, 8, 4), Table 1 is not proportional.

Step2: Check Table 2 for Proportionality

For \( x = 5, y = 15 \): \( \frac{15}{5} = 3 \)
For \( x = 8, y = 24 \): \( \frac{24}{8} = 3 \)
For \( x = 11, y = 33 \): \( \frac{33}{11} = 3 \)
Since \( \frac{y}{x} = 3 \) (constant), Table 2 is proportional, and \( y = 3x \).

Answer:

Table 1: Not proportional
Table 2: Proportional, \( y \) is \( \boldsymbol{3} \) times \( x \)