Question

t.2 identify proportional relationships from tables select the tables that show a proportional relationship between x and y.

Explanation:

Step1: Recall proportional relationship rule

A proportional relationship between \(x\) and \(y\) means \(y = kx\) (where \(k\) is a constant), so \(\frac{y}{x}=k\) (constant) for all non - zero \(x\).

Step2: Check the first table

For the first table with \(x = 3,y = 5\), \(\frac{y}{x}=\frac{5}{3}\); when \(x = 6,y = 10\), \(\frac{y}{x}=\frac{10}{6}=\frac{5}{3}\); when \(x = 9,y = 15\), \(\frac{y}{x}=\frac{15}{9}=\frac{5}{3}\). The ratio \(\frac{y}{x}\) is constant (\(k=\frac{5}{3}\)), so this table shows a proportional relationship.

Step3: Check the second table

For the second table with \(x = 1,y = 1\), \(\frac{y}{x}=\frac{1}{1}=1\); when \(x = 2,y = 2\), \(\frac{y}{x}=\frac{2}{2}=1\); when \(x = 5,y = 5\), \(\frac{y}{x}=\frac{5}{5}=1\). The ratio \(\frac{y}{x}\) is constant (\(k = 1\)), so this table also shows a proportional relationship.

Answer:

Both tables (the one with \(x = 3,6,9\) and \(y = 5,10,15\) and the one with \(x = 1,2,5\) and \(y = 1,2,5\)) show a proportional relationship between \(x\) and \(y\).