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 linear function has a positive slope, let's analyze each option:

1. **Line through points (0, 3) and (4, 2)**:
The slope (m) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, using the points (0, 3) and (4, 2):
\[
m = \frac{2 - 3}{4 - 0} = \frac{-1}{4} = -0.25
\]
The slope is negative.

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

3. **First Table**:
To find the slope from the table entries, we can calculate it using two points, for example, \((0, 1.0)\) and \((2, 1.5)\):
\[
m = \frac{1.5 - 1.0}{2 - 0} = \frac{0.5}{2} = 0.25
\]
The slope is positive.

4. **Second Table**:
To find the slope from this table, let's take the two points \((1, 2.4)\) and \((7, -1.2)\):
\[
m = \frac{-1.2 - 2.4}{7 - 1} = \frac{-3.6}{6} = -0.6
\]
The slope is negative.

Based on this analysis, the function with a positive slope is from the **first table**.