To determine the correct statement that describes the slope of a graph of the data showing the relationship between the weight and price of pumpkins, let's analyze the data:
Given data:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Weight (lb)} & \text{Price (\$)} \\
\hline
4 & 6 \\
\hline
8 & 12 \\
\hline
12 & 18 \\
\hline
16 & 24 \\
\hline
20 & 30 \\
\hline
\end{array}
\][/tex]
First, we need to calculate the slope, which in this context is the rate of change of price with respect to weight. This is commonly given by the formula:
[tex]\[
\text{slope} = \frac{\Delta \text{Price}}{\Delta \text{Weight}}
\][/tex]
We can choose any two consecutive points from the data to calculate the slope. Let's use the first pair of data points:
[tex]\[
\text{Weight}_1 = 4 \, \text{lb}, \, \text{Price}_1 = \$6
\][/tex]
[tex]\[
\text{Weight}_2 = 8 \, \text{lb}, \, \text{Price}_2 = \$12
\][/tex]
The change in weight ([tex]\(\Delta \text{Weight}\)[/tex]) is:
[tex]\[
\Delta \text{Weight} = \text{Weight}_2 - \text{Weight}_1 = 8 - 4 = 4 \, \text{lb}
\][/tex]
The change in price ([tex]\(\Delta \text{Price}\)[/tex]) is:
[tex]\[
\Delta \text{Price} = \text{Price}_2 - \text{Price}_1 = 12 - 6 = 6 \, \text{\$}
\][/tex]
Now we can calculate the slope:
[tex]\[
\text{slope} = \frac{\Delta \text{Price}}{\Delta \text{Weight}} = \frac{6 \, \$}{4 \, \text{lb}} = 1.5 \, \frac{\$}{\text{lb}}
\][/tex]
This means for each additional pound, the price increases by \[tex]$1.50.
Thus, the correct statement is:
For each additional pound, the price increases \$[/tex]1.50.
