You can make 7 gal of liquid fertilizer by mixing 10 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?
To represent the relation between the teaspoons of powder used and the gallons of fertilizer made, we can create a table:
Teaspoons of powder used (x) | Gallons of fertilizer made (y)
-------------------------------------|----------------------------------------
10 | 7
From the given information, we can see that when 10 teaspoons of powder are used, 7 gallons of fertilizer are made.
Now, let's write an equation to represent the relationship. We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Since we only have one data point, it is impossible to determine the slope m. However, we can determine the y-intercept b.
Using the given information: (10, 7), we can substitute those values into the equation:
7 = m(10) + b
To find the value of b, we can subtract m(10) from both sides:
7 - 10m = b
Now, let's graph this relation. On the x-axis, we'll represent the teaspoons of powder used, and on the y-axis, we'll represent the gallons of fertilizer made. We only have one data point, so we'll plot the point (10, 7).
Graph:
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0 10 ... ... ...
Now, let's discuss whether the amount of fertilizer made is a function of the amount of powder used.
In this scenario, we can say that the amount of fertilizer made is a function of the amount of powder used. Since there is a unique output (gallons of fertilizer) for each input (teaspoons of powder), the relation between the two can be considered a function.
Represent the relation using an equation.
y = [ ]
(Simplify your answer. Type an expression using x as the variable. Use integers or fractions for any numbers in the expression.)
To represent the relation using an equation, we need to determine the equation that relates the teaspoons of powder used (x) with the gallons of fertilizer made (y).
From the given information, we know that when 10 teaspoons of powder are used, 7 gallons of fertilizer are made. This gives us one data point: (x=10, y=7).
To determine the equation, we can use the point-slope form of a linear equation, which is given as:
y - y₁ = m(x - x₁)
Where (x₁, y₁) represents a point on the line and m represents the slope.
Using the data point (x₁=10, y₁=7), we can substitute it into the point-slope form:
y - 7 = m(x - 10)
Now, let's find the value of m. We can calculate the slope using the formula:
m = (y₂ - y₁)/(x₂ - x₁)
Since we only have one data point, we cannot determine the slope. Therefore, we will leave it as m for now:
y - 7 = m(x - 10)
Finally, our equation representing the relation between the teaspoons of powder used (x) and the gallons of fertilizer made (y) is:
y - 7 = m(x - 10)
Note: Without additional data points, it is not possible to determine the specific equation.
To represent the relation between the teaspoons of powder used and the gallons of fertilizer made, we can create a table, an equation, and a graph.
1. Table:
Let's create a table that shows the number of teaspoons of powder used (x) and the corresponding gallons of fertilizer made (y):
| Teaspoons of Powder (x) | Gallons of Fertilizer (y) |
|-------------------------|--------------------------|
| 10 | 7 |
2. Equation:
We can express the relation between the teaspoons of powder used and the gallons of fertilizer made using an equation. In this case, since the ratio of 10 teaspoons of powder to 7 gallons of fertilizer is constant, it means the relationship is linear (a straight line).
We can write the equation in the form y = mx + b, where m represents the slope (the rate at which y changes with respect to x) and b represents the y-intercept (the value of y when x equals 0).
In this case, the equation would be: y = (7/10)x + b. However, since we don't have enough information to determine b (the y-intercept), we cannot write the exact equation for this relation.
3. Graph:
We can plot the data from the table onto a graph. The x-axis represents the teaspoons of powder used, and the y-axis represents the gallons of fertilizer made. We plot the point (10, 7) on the graph.
The graph would look like a single point on the coordinate plane, as there is only one data point.
Now, regarding your question about whether the amount of fertilizer made is a function of the amount of powder used, the answer is yes. In this case, since each teaspoon of powder consistently produces the same amount of gallons of fertilizer, there is a clear one-to-one correspondence between the teaspoons of powder used and the gallons of fertilizer made, making it a function.