Question

Which of the following tables represent a linear function with the same slope as y = 2 - 3x ?

Select 2 that apply.

(2 points)
Responses

Answer 1

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):
\[
\text{slope} = \frac{-4 - (-1)}{2 - 1} = \frac{-3}{1} = -3
\]

- 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):
\[
\text{slope} = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3
\]

- 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.