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

x:4, -1
y:0, 2

1 answer

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

The given points are:

  1. \( (4, 0) \)
  2. \( (-1, 2) \)

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using our points:

  • \( (x_1, y_1) = (4, 0) \)
  • \( (x_2, y_2) = (-1, 2) \)

Substituting these values into the slope formula, we get:

\[ m = \frac{2 - 0}{-1 - 4} = \frac{2}{-5} = -\frac{2}{5} \]

Since we have a consistent slope, the table represents a linear function, and the slope is \( -\frac{2}{5} \).