Question

select the tables that show a proportional relationship between x and y. work it out not feeling ready yet? these can help: find the constant of proportionality from a table lesson: proportional relationships

Explanation:

Step1: Check the first table

For the first table, when \(x = 8\), \(y = 8\), \(\frac{y}{x}=\frac{8}{8} = 1\); when \(x = 10\), \(y = 10\), \(\frac{y}{x}=\frac{10}{10}=1\); when \(x = 12\), \(y = 12\), \(\frac{y}{x}=\frac{12}{12}=1\). The ratio \(\frac{y}{x}\) is constant (\(k = 1\)).

Step2: Check the second table

For the second table, when \(x = 1\), \(y = 5\), \(\frac{y}{x}=\frac{5}{1}=5\); when \(x = 2\), \(y = 8\), \(\frac{y}{x}=\frac{8}{2} = 4\); when \(x = 5\), \(y = 17\), \(\frac{y}{x}=\frac{17}{5}=3.4\). The ratio \(\frac{y}{x}\) is not constant.

Answer:

Only the first table (with \(x = 8,y = 8\); \(x = 10,y = 10\); \(x = 12,y = 12\)) shows a proportional relationship.