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does this table represent a linear function if so state so and state the slope

x:-4, -1
y:2, 8

1 answer

To determine if the given points represent a linear function, we can check if the slope between the two points is constant.

The points given are (-4, 2) and (-1, 8).

  1. Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

    Here, \( (x_1, y_1) = (-4, 2) \) and \( (x_2, y_2) = (-1, 8) \).

    Plugging in the values: \[ m = \frac{8 - 2}{-1 - (-4)} = \frac{6}{3} = 2 \]

Since the slope is constant, the table does represent a linear function.

  1. State: Yes, this table represents a linear function.

  2. State the slope: The slope \( m \) is 2.