You can make 3 gal of liquid fertilizer by mixing 11 tsp of powdered 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?
We can represent the relation between the teaspoons of powder used and the gallons of fertilizer made using a table, an equation, and a graph.
Table:
Let's create a table to illustrate the relation:
| Teaspoons of Powder (tsp) | Gallons of Fertilizer (gal) |
|--------------------------|----------------------------|
| 11 | 3 |
Equation:
Let's represent the equation for this relation. Since the given ratio is 11 tsp of powder to 3 gallons of fertilizer, we can say that the number of gallons (G) is a function of the number of teaspoons (T), represented as:
G = 3/11 * T
Graph:
We can plot a graph to visually represent this relation. On the x-axis, we'll have the number of teaspoons of powder used, and on the y-axis, we'll have the gallons of fertilizer made. The graph will show us the values of the relation.
The graph of the equation G = 3/11 * T will represent a straight line passing through the point (11, 3).
Is the amount of fertilizer made a function of the amount of powder used?
Yes, the amount of fertilizer made (gallons) is a function of the amount of powder used (teaspoons). In this case, the function is a linear function. Each value of teaspoons of powder corresponds to only one value of gallons of fertilizer, satisfying the definition of a function.