Practice finding and using the constant of proportionality.

\begin{tabular}{|c|c|}
\hline
Number of Baseballs & [tex]$\operatorname{cost}(\$[/tex])[tex]$ \\
\hline
10 & 5 \\
\hline
12 & 6 \\
\hline
22 & 11 \\
\hline
\end{tabular}

Use the table to find the constant of proportionality for the ratio of cost to baseballs. $[/tex]\square$



Answer :

To determine the constant of proportionality, we need to look at the ratio of the cost to the number of baseballs.

First, let's determine the ratio for the given data points:

1. For 10 baseballs costing [tex]$5: \[ \frac{\text{Cost}}{\text{Number of Baseballs}} = \frac{5}{10} = 0.5 \] 2. For 12 baseballs costing $[/tex]6:
[tex]\[ \frac{\text{Cost}}{\text{Number of Baseballs}} = \frac{6}{12} = 0.5 \][/tex]

3. For 22 baseballs costing $11:
[tex]\[ \frac{\text{Cost}}{\text{Number of Baseballs}} = \frac{11}{22} = 0.5 \][/tex]

In each case, the ratio of the cost to the number of baseballs is the same, which confirms that the relationship between the cost and the number of baseballs is proportional.

Therefore, the constant of proportionality is:
[tex]\[ \boxed{0.5} \][/tex]