Questions: Two Graphs for Each Relationship At an animal shelter, a guinea pig eats cabbage at the constant rate. The table shows the proportional relationship between minutes and pieces of cabbage eaten. 15 3 25 5 35 7 45 9 55 11 The constant of proportionality is 1 2 3 4 5 6 7 8 9

Solution Steps

The table shows a proportional relationship between minutes and pieces of cabbage eaten. The relationship can be expressed as: \[ \text{Pieces of cabbage} = k \cdot \text{Minutes} \] where \( k \) is the constant of proportionality.

To find \( k \), we can use any row from the table. Let's use the first row: \[ 3 = k \cdot 15 \] Solving for \( k \): \[ k = \frac{3}{15} = 0.2 \]

We can verify \( k \) using another row from the table. Let's use the second row: \[ 5 = k \cdot 25 \] Solving for \( k \): \[ k = \frac{5}{25} = 0.2 \] The constant of proportionality is consistent across the table.

Final Answer