Question

Which linear functions represent a slope of 4? Check all that apply.
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 6, 9, 12. Column 2 is labeled y with entries negative 11, 1, 13, 25.
On a coordinate plane, a line goes through points (0, 3) and (5, 4).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 1, 3, 7. Column 2 is labeled y with entries negative 32, 24, 16, 8.
On a coordinate plane, a line goes through points (2, 0) and (3, 4).

Answer 1

To determine which linear functions represent a slope of 4, we need to calculate the slope of the lines represented by the provided tables and points, and check whether the slope equals 4.

1. **First Table**:
- Points: (3, -11), (6, 1), (9, 13), (12, 25)
- Slope calculation:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using points (3, -11) and (6, 1):
\[
\text{slope} = \frac{1 - (-11)}{6 - 3} = \frac{1 + 11}{3} = \frac{12}{3} = 4
\]

✅ Represents a slope of 4.

2. **First Coordinate Plane**:
- Points: (0, 3) and (5, 4)
- Slope calculation:
\[
\text{slope} = \frac{4 - 3}{5 - 0} = \frac{1}{5}
\]

❌ Does not represent a slope of 4.

3. **Second Table**:
- Points: (-5, -32), (-1, 24), (3, 16), (7, 8)
- Slope calculation:
Using points (-5, -32) and (-1, 24):
\[
\text{slope} = \frac{24 - (-32)}{-1 - (-5)} = \frac{24 + 32}{4} = \frac{56}{4} = 14
\]

❌ Does not represent a slope of 4.

4. **Second Coordinate Plane**:
- Points: (2, 0) and (3, 4)
- Slope calculation:
\[
\text{slope} = \frac{4 - 0}{3 - 2} = \frac{4}{1} = 4
\]

✅ Represents a slope of 4.

### Summary:
The functions that represent a slope of 4 are:
- The first table.
- The second coordinate plane.