Question

Which linear function has a positive slope?
On a coordinate plane, a line goes through points (0, 3) and (4, 2).
y = negative 0.1 x minus 5
A 2-column table with 5 rows. Column 1 is labeled x with entries negative 4, negative 2, 0, 2, 4. Column 2 is labeled y with entries 0, 0.5, 1.0, 1.5, 2.0.
A 2-column table with 5 rows. Column 1 is labeled x with entries negative 6, negative 2, 1, 7, 9. Column 2 is labeled y with entries 6.6, 4.2, 2.4, negative 1.2, negative 2.4.

Answer 1

To determine which of the provided functions has a positive slope, we can analyze the slope of each one.

1. **Line through points (0, 3) and (4, 2)**:
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting in the points:
\[
m = \frac{2 - 3}{4 - 0} = \frac{-1}{4} = -0.25
\]
This slope is negative.

2. **Function**: \( y = -0.1x - 5 \)
The slope of this function is \(-0.1\), which is also negative.

3. **First table**:
Analyzing the values in the first table:
- As \( x \) increases from -4 to 4, \( y \) increases from 0 to 2. This shows an upward trend, meaning the slope is positive.

4. **Second table**:
Analyzing the values in the second table:
- As \( x \) increases from -6 to 9, \( y \) decreases from 6.6 to -2.4. This shows a downward trend, meaning the slope is negative.

### Conclusion:
- The linear function with a positive slope is represented by the **first table**, where the values of \( y \) increase as \( x \) increases.