Question

1. circle the table or tables that show a proportional relationship. show your work to justify your answer.

Explanation:

Step1: Define proportionality

A relationship is proportional if the ratio of the two columns is constant for all rows, i.e., $\frac{y}{x} = k$ (constant) for every pair $(x,y)$.

Step2: Check first table

Calculate ratios:
$\frac{4}{1}=4$, $\frac{8}{2}=4$, $\frac{16}{4}=4$, $\frac{20}{5}=4$
All ratios equal 4 (constant).

Step3: Check second table

Calculate ratios:
$\frac{3}{2}=1.5$, $\frac{6}{3}=2$, $\frac{9}{6}=1.5$, $\frac{12}{8}=1.5$
Ratios are not consistent (1.5 and 2 differ).

Step4: Check third table

Calculate ratios:
$\frac{2}{1}=2$, $\frac{6}{3}=2$, $\frac{10}{5}=2$, $\frac{14}{7}=2$
All ratios equal 2 (constant).

Answer:

The first and third tables show a proportional relationship.