To determine which tables represent a linear function with the same slope as \( y = 2 - 3x \), we first identify the slope of this equation. The slope-intercept form of a linear equation is \( y = mx + b \), where \( m \) is the slope. The equation given is in the form:
\[ y = -3x + 2 \]
From this, we see that the slope \( m = -3 \).
For a table of values to represent a linear function with the same slope, the change in \( y \) divided by the change in \( x \) between any two points must equal \(-3\).
Now, let's analyze two tables (assuming you provide them). For demonstration, I will create an example to illustrate how to check for slope:
Example Table 1:
\[ \begin{array}{|c|c|} \hline x & y \ \hline 1 & -1 \ 2 & -4 \ 3 & -7 \ \hline \end{array} \]
Calculating the slope:
-
From (1, -1) to (2, -4): \[ \text{slope} = \frac{-4 - (-1)}{2 - 1} = \frac{-3}{1} = -3 \]
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From (2, -4) to (3, -7): \[ \text{slope} = \frac{-7 - (-4)}{3 - 2} = \frac{-3}{1} = -3 \]
Example Table 2:
\[ \begin{array}{|c|c|} \hline x & y \ \hline 0 & 2 \ 1 & -1 \ 2 & -4 \ \hline \end{array} \]
Calculating the slope:
-
From (0, 2) to (1, -1): \[ \text{slope} = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \]
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From (1, -1) to (2, -4): \[ \text{slope} = \frac{-4 - (-1)}{2 - 1} = \frac{-3}{1} = -3 \]
Conclusion
Both tables would represent linear functions with the same slope as \( y = 2 - 3x \).
If you provide specific tables or data, I can help you analyze and find the correct answers tailored to those tables.