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Math  /  Data & Statistics

QuestionSelect the tables that show a proportional relatlonship between xx and yy. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 2 & 3 \\ \hline 4 & 6 \\ \hline 12 & 18 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 6 & 3 \\ \hline 12 & 6 \\ \hline 14 & 7 \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. A proportional relationship between x x and y y means that the ratio yx \frac{y}{x} is constant for all pairs.
2. Each table needs to be evaluated separately to determine if the relationship is proportional.

STEP 2

1. Evaluate the first table for a constant ratio.
2. Evaluate the second table for a constant ratio.

STEP 3

Calculate the ratio yx \frac{y}{x} for each pair in the first table:
32=1.5,64=1.5,1812=1.5\frac{3}{2} = 1.5, \quad \frac{6}{4} = 1.5, \quad \frac{18}{12} = 1.5

STEP 4

Calculate the ratio yx \frac{y}{x} for each pair in the second table:
36=0.5,612=0.5,714=0.5\frac{3}{6} = 0.5, \quad \frac{6}{12} = 0.5, \quad \frac{7}{14} = 0.5
The first table shows a proportional relationship because the ratio yx \frac{y}{x} is constant at 1.5. The second table also shows a proportional relationship because the ratio yx \frac{y}{x} is constant at 0.5.
Both tables show a proportional relationship.

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