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

x:-1,1,3,5
y:1,-3,-7,-11

1 answer

To determine if the table represents a linear function, we need to check if the change in \( y \) divided by the change in \( x \) (the slope) is constant.

Given the data points:

  • \( (-1, 1) \)
  • \( (1, -3) \)
  • \( (3, -7) \)
  • \( (5, -11) \)

Let's calculate the slope between each pair of consecutive points:

  1. From \((-1, 1)\) to \( (1, -3)\): \[ \text{slope} = \frac{-3 - 1}{1 - (-1)} = \frac{-4}{2} = -2 \]

  2. From \( (1, -3)\) to \( (3, -7)\): \[ \text{slope} = \frac{-7 - (-3)}{3 - 1} = \frac{-4}{2} = -2 \]

  3. From \( (3, -7)\) to \( (5, -11)\): \[ \text{slope} = \frac{-11 - (-7)}{5 - 3} = \frac{-4}{2} = -2 \]

Since the slope is consistently \(-2\) for each pair of points, the table does represent a linear function.

Conclusion: Yes, the table represents a linear function with a slope of \(-2\).