Question

You can make 4 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?

Answer 1

To represent the relationship between the teaspoons of powdered fertilizer used and the gallons of liquid fertilizer made, we can use a table, an equation, and a graph.

### Table

We know that 11 teaspoons of powdered fertilizer make 4 gallons of liquid fertilizer. To get various combinations, we can assume a linear relationship. The ratio of liquid fertilizer to powdered fertilizer can be expressed with the following values:

| Teaspoons of Powder (t) | Gallons of Fertilizer (g) |
|-------------------------|---------------------------|
| 0 | 0 |
| 11 | 4 |
| 22 | 8 |
| 33 | 12 |

### Equation

From the table, we can see that for every 11 teaspoons of powdered fertilizer used, we get 4 gallons of liquid fertilizer. We can express this as a linear equation:

\[
g = \frac{4}{11} t
\]

Where:
- \( g \) is the gallons of liquid fertilizer,
- \( t \) is the teaspoons of powdered fertilizer.

### Graph

To graph this relationship, plot the points from the table on a coordinate system where the x-axis represents teaspoons of powdered fertilizer (t) and the y-axis represents gallons of fertilizer (g). The points you would plot from the table are:

1. (0, 0)
2. (11, 4)
3. (22, 8)
4. (33, 12)

Connect these points with a straight line, as the relationship is linear.

### Function Determination

To determine if the amount of fertilizer made is a function of the amount of powder used, we need to see if every input (teaspoon of powder) corresponds to exactly one output (gallon of fertilizer).

Since the equation is linear and has a unique y-value (gallons of fertilizer) for each x-value (teaspoons of powder), we can conclude that:

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