To determine which table represents the relation between teaspoons of powdered fertilizer used and gallons of fertilizer made, we start by noting that mixing 9 teaspoons of powdered fertilizer produces 5 gallons of liquid fertilizer.
Key Observations:
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Proportion: The relationship is directly proportional. For every 9 teaspoons of powdered fertilizer, 5 gallons are produced.
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Ratio: We can derive a formula based on that proportion:
\[ \text{Gallons} = \frac{5}{9} \times \text{Teaspoons} \]
Let's analyze the options in the tables:
A:
- \( 0 \text{ tsp} \rightarrow 0 \text{ gal} \)
- \( 5 \text{ tsp} \rightarrow 9 \text{ gal} \) (incorrect, should be less than 5)
- \( 9 \text{ tsp} \rightarrow 5 \text{ gal} \) (correct)
- \( 10 \text{ tsp} \rightarrow 18 \text{ gal} \) (incorrect, proportion wrong)
This table is inconsistent and therefore invalid.
B:
- \( 0 \text{ tsp} \rightarrow 0 \text{ gal} \)
- \( 9 \text{ tsp} \rightarrow 5 \text{ gal} \) (correct)
- \( 18 \text{ tsp} \rightarrow 10 \text{ gal} \) (incorrect)
- \( 27 \text{ tsp} \rightarrow 15 \text{ gal} \) (incorrect)
This table appears inconsistent with the linear relationship derived earlier.
C:
- \( 0 \text{ gal} \rightarrow 15 \text{ tsp} \) (incorrect)
- \( 9 \text{ gal} \rightarrow 10 \text{ tsp} \) (incorrect)
- \( 18 \text{ gal} \rightarrow 5 \text{ tsp} \) (incorrect)
- \( 27 \text{ gal} \rightarrow 0 \text{ tsp} \) (incorrect)
This table is also incorrect.
Conclusion on Tables:
None of the tables (A, B, or C) correctly represent the relationship between teaspoons used and gallons produced.
Equation:
The equation to represent the relationship is:
\[ y = \frac{5}{9}x \]
Where \(y\) = gallons of fertilizer and \(x\) = teaspoons of powdered fertilizer.
Function Analysis:
To determine if the amount of fertilizer made is a function of the amount of powder used, we check if each input (teaspoons of powder) corresponds to only one output (gallons of fertilizer). Given the direct proportionality here, it satisfies the definition of a function.
Graph:
To graph the equation:
- Plot points based on the equation or relation, like:
- (0, 0)
- (9, 5)
- (18, 10)
- (27, 15)
- Draw a line through the points.
Final Thought:
Based on the original scenario and calculations, you may want to revisit the tables presented or create your own based on the relationship defined by the equation derived.