Question

Compare the two linear functions.

A 2-column table with 5 rows. Column 1 is labeled x with entries negative 3, negative 1, 2, 5, 10. Column 2 is labeled y with entries 8.5, 5.5, 1, negative 3.5, negative 11. On a coordinate plane, a line goes through points (negative 3, 0) and (2, 0).

Identify the slope of the line given in the table:
Identify the slope of the line given in the graph:
Which linear function has a negative slope?
Which linear function has the steeper slope?

Answer 1

To analyze and compare the two linear functions given by the table and the graph, we will first calculate the slope of each.

### For the table:

The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

From the table, we can select two points. Let’s use:
- Point 1: \((-3, 8.5)\)
- Point 2: \((10, -11)\)

Calculating the slope:

\[
m = \frac{-11 - 8.5}{10 - (-3)} = \frac{-19.5}{13} \approx -1.5
\]

### For the graph:

The line passes through the points \((-3, 0)\) and \( (2, 0) \). To find the slope:

- Point 1: \((-3, 0)\)
- Point 2: \((2, 0)\)

Calculating the slope:

\[
m = \frac{0 - 0}{2 - (-3)} = \frac{0}{5} = 0
\]

### Summary of findings:

1. **Slope of the line given in the table:** Approximately \(-1.5\)
2. **Slope of the line given in the graph:** \(0\)
3. **Which linear function has a negative slope?** The function represented by the table.
4. **Which linear function has the steeper slope?** The function from the table has a steeper slope since \(-1.5\) (the absolute value is 1.5) is steeper than \(0\).

### Final Answers:
- Slope of the line given in the table: \(-1.5\)
- Slope of the line given in the graph: \(0\)
- Linear function with a negative slope: **Table function**
- Steeper slope: **Table function**