Certainly! Let's take a detailed look at the table and the corresponding information to determine what conclusions can be drawn.
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Gallons, } g & \text{Liters, } l \\
\hline
1 & 3.79 \\
\hline
2 & 7.58 \\
\hline
3 & 11.37 \\
\hline
4 & 15.16 \\
\hline
5 & 18.95 \\
\hline
6 & 22.74 \\
\hline
\end{array}
\][/tex]
1. The independent variable is the number of gallons:
The independent variable is the one that is being manipulated or controlled in an experiment or scenario. In this table, the number of gallons \( g \) is the independent variable because this is what we are inputting or changing.
2. Liters is a function of Gallons:
The dependent variable is the one that depends on the independent variable. Here, the amount of liters \( l \) depends on the number of gallons \( g \). Therefore, liters can be considered a function of gallons.
3. The equation \( l = 3.79 g \) represents the table:
When we look at the table, we see that for each gallon value \( g \), the corresponding liters \( l \) is given. If we multiply each gallon value by 3.79, the result matches the liters value exactly:
[tex]\[
\begin{align*}
1 \cdot 3.79 &= 3.79 \\
2 \cdot 3.79 &= 7.58 \\
3 \cdot 3.79 &= 11.37 \\
4 \cdot 3.79 &= 15.16 \\
5 \cdot 3.79 &= 18.95 \\
6 \cdot 3.79 &= 22.74 \\
\end{align*}
\][/tex]
Therefore, the equation \( l = 3.79 g \) accurately represents the relationship between gallons and liters in the table.
4. As the number of gallons increases, the number of liters increases:
Observing the table, it is clear that as the number of gallons (\( g \)) increases, so does the value of liters (\( l \)). This indicates a direct relationship where an increase in the independent variable leads to an increase in the dependent variable.
5. This is a function because every input has exactly one output:
In the table, each value of \( g \) (gallons) corresponds to exactly one value of \( l \) (liters). This meets the definition of a function, where every input has a unique output.
Thus, the correct statements we can determine from the table are:
- The independent variable is the number of gallons.
- Liters is a function of Gallons.
- The equation \( l = 3.79 g \) represents the table.
- As the number of gallons increases, the number of liters increases.
- This is a function because every input has exactly one output.
