To determine the linear equations represented by the given table of values, let's assume "x" is the independent variable and "y" is the dependent variable.
The table of values is as follows:
\[ \begin{array}{|c|c|} \hline x & y \ \hline 0 & 3 \ 1 & 6 \ 2 & 9 \ \hline \end{array} \]
To derive the linear equation, we can observe the changes in y with respect to x:
- When \( x = 0 \), \( y = 3 \)
- When \( x = 1 \), \( y = 6 \)
- When \( x = 2 \), \( y = 9 \)
Next, we need to determine the slope \( m \) of the line (change in \( y \) over change in \( x \)):
\[ m = \frac{\Delta y}{\Delta x} = \frac{6 - 3}{1 - 0} = \frac{3}{1} = 3 \]
Now that we have the slope, we can use the point-slope form of the line equation:
\[ y - y_1 = m(x - x_1) \]
Using the point \((0, 3)\):
\[ y - 3 = 3(x - 0) \ y - 3 = 3x \ y = 3x + 3 \]
So the linear equation that represents these values is:
\[ y = 3x + 3 \]
If you have more values or a more complex table to analyze, please provide the extra context or data, and I can help further!