Question

A 2-column table with 4 rows. Column 1 is labeled x with entries 5, 3, negative 1, negative 2. Column 2 is labeled y with entries 6, 2, negative 6, negative 8. On a coordinate plane, a line goes through points (negative 2, 4) and (0, negative 4).
Linear functions are expressed by data in a table and by a graph. Select all that apply.
The slope is the same for both functions.
The function expressed in the graph has a steeper slope than the function in the table.
The y-intercept is the same for both functions.
The table and the graph express an equivalent function.

Answer 1

To analyze the statements, let's first find the slope (m) of the linear function represented by the points in the table and then determine the slope of the function represented by the line on the graph.

### 1. Analyzing the table function
For the points in the table:
- \( (5, 6) \)
- \( (3, 2) \)
- \( (-1, -6) \)
- \( (-2, -8) \)

Let's calculate the slope using two adjacent points from the table, say \( (5, 6) \) and \( (3, 2) \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 6}{3 - 5} = \frac{-4}{-2} = 2
\]

Now, let's check another pair, say \( (-2, -8) \) and \( (-1, -6) \):

\[
m = \frac{-6 - (-8)}{-1 - (-2)} = \frac{2}{1} = 2
\]

The slope for the function expressed in the table is consistent at \( 2 \).

### 2. Analyzing the graph function
The equation of the line through the points \( (-2, 4) \) and \( (0, -4) \):

Using the slope formula:

\[
m = \frac{-4 - 4}{0 - (-2)} = \frac{-8}{2} = -4
\]

### Summary of Analysis
- **Slope of table function**: \( 2 \)
- **Slope of graph function**: \( -4 \)

### Evaluating the Statements
1. **The slope is the same for both functions.**
**False.** (Slope of table is \( 2 \), slope of graph is \( -4 \))

2. **The function expressed in the graph has a steeper slope than the function in the table.**
**False.** (The absolute value of the graph's slope (\( 4 \)) is greater than the table's slope (\( 2 \)). This means the graph has a steeper slope, but since it's negative, its steepness cannot be directly compared without context regarding direction).

3. **The y-intercept is the same for both functions.**
**False.** (The y-intercept for the table can be determined by extending \( y = 2x + b \) to find \( b \) which is not clear from the given points. The looser conclusion here suggests they differ; for the graph, the y-intercept is \( -4 \).)

4. **The table and the graph express an equivalent function.**
**False.** (They have different slopes, indicating different functions.)

### Conclusions
None of the statements apply based on the analysis:
- **All selected statements are false.**