Question

You can make 3 gal of liquid fertilizer by mixing 11 tsp of powdered fertilizer with water. Represent the relation between the teaspoons of powder used and the gallons of fertilizer made using a​ table, an​ equation, and a graph. Is the amount of fertilizer made a function of the amount of powder​ used?
Question content area bottom
Part 1
Which table below represents the​ relation?
A.
Number of​ tsp, x
Number of​ gal, y
0
0
3
11
6
22
9
33
B.
Number of​ tsp, x
Number of​ gal, y
0
0
11
3
22
6
33
9
C.
Number of​ gal, x
Number of​ tsp, y
0
9
11
6
22
3
33
0

Answer 1

To represent the relation between the teaspoons of powder used (x) and the gallons of fertilizer made (y), you will first need to determine the relationship based on the given information.

You can make 3 gallons of fertilizer using 11 teaspoons of powdered fertilizer. Thus, the ratio of teaspoons to gallons is:

\[
\text{Gallons of fertilizer} = \frac{\text{Teaspoons of powdered fertilizer}}{11} \times 3
\]

This simplifies to:

\[
y = \frac{3}{11} x
\]

Where:
- \( y \) = gallons of fertilizer made
- \( x \) = teaspoons of powdered fertilizer used

### Creating the Table

Using the equation \( y = \frac{3}{11} x \), you can create a table of values for different amounts of teaspoons of powder:

| Number of tsp, \( x \) | Number of gal, \( y \) |
|------------------------|------------------------------|
| 0 | 0 |
| 11 | 3 |
| 22 | 6 |
| 33 | 9 |

### Conclusion of Part 1

Among the options A, B, and C, the table that correctly represents the relation is:

**A.**
| Number of tsp, \( x \) | Number of gal, \( y \) |
|-----------------------|------------------------|
| 0 | 0 |
| 11 | 3 |
| 22 | 6 |
| 33 | 9 |

### Part 2 - Equation Representation

Based on the previously discussed relationship, the equation representing this relationship is:

\[
y = \frac{3}{11} x
\]

### Part 3 - Graph Representation

To graph this relation, you will plot the points from the table on a Cartesian coordinate system, where the x-axis represents teaspoons of powder and the y-axis represents gallons of fertilizer. Here are the points to plot:

- (0, 0)
- (11, 3)
- (22, 6)
- (33, 9)

### Function Check

To determine if the amount of fertilizer made is a function of the amount of powder used, you check if for every input \( x \) (number of teaspoons), there is exactly one output \( y \) (number of gallons). In this case, there is a clear, consistent relationship, fulfilling the definition of a function.

### Final Conclusion

Yes, the amount of fertilizer made is a function of the amount of powder used.

If you need the graph or further assistance, let me know!