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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).

1 answer

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.