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The tables show linear functions representing the cost for purchasing different amounts of broccoli and cauliflower.

Broccoli
\begin{tabular}{|l|c|c|c|c|}
\hline Amount (lbs) & 2.5 & 3 & 3.25 & 4.15 \\
\hline Cost (\$) & 3.00 & 3.60 & 3.90 & 4.98 \\
\hline
\end{tabular}

Cauliflower
\begin{tabular}{|l|c|c|c|c|}
\hline Amount (lbs) & 2.75 & 3.2 & 3.85 & 4.5 \\
\hline Cost (\$) & 2.75 & 3.20 & 3.85 & 4.50 \\
\hline
\end{tabular}

Which function has the greater slope and what does it indicate?

A. The broccoli function has the greater slope, which shows that the cost per pound of broccoli is less than the cost per pound of cauliflower.

B. The broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.

C. The cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is less than the cost per pound of broccoli.

D. The cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is greater than the cost per pound of broccoli.

Sagot :

GinnyAnswer
To determine which function has the greater slope and interpret its meaning, we'll analyze the data for both broccoli and cauliflower.

### Broccoli Data:
- Amounts (lbs): 2.5, 3, 3.25, 4.15
- Costs ($): 3.00, 3.60, 3.90, 4.98

### Cauliflower Data:
- Amounts (lbs): 2.75, 3.2, 3.85, 4.5
- Costs ($): 2.75, 3.20, 3.85, 4.50

### Step-by-Step Solution:

1. Identify Linear Relationships:
Both tables represent linear functions, as we can infer from the consistent change in amounts and costs.

2. Calculate the Slope:
The slope of a linear function representing cost per amount (pound) can be determined using the least squares method. The slope (m) gives us the rate of change of cost with respect to the amount.

3. Slopes Obtained:
- Broccoli function slope (cost per pound): 1.2
- Cauliflower function slope (cost per pound): 1.0

4. Interpret the Meaning:
- A greater slope indicates a higher cost per pound.
- Since the slope for broccoli is greater (1.2) than the slope for cauliflower (1.0), it shows that the cost per pound of broccoli is higher than the cost per pound of cauliflower.

### Conclusion:
The correct statement is:
"The broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower."

Therefore, the right answer is:
The broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.
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