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

Question

x:-2,0,2
y:7,1,-5

Answer 1

To determine if the table represents a linear function, we can check if the changes in \( y \) (the output) are consistent with the changes in \( x \) (the input).

Let's examine the given points:

1. \( (-2, 7) \)
2. \( (0, 1) \)
3. \( (2, -5) \)

Now, we can calculate the slope \( m \) between each pair of points.

Using the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Calculating the slope between the first two points \((-2, 7)\) and \((0, 1)\): \[ m_1 = \frac{1 - 7}{0 - (-2)} = \frac{-6}{2} = -3 \]

Calculating the slope between the second two points \((0, 1)\) and \((2, -5)\): \[ m_2 = \frac{-5 - 1}{2 - 0} = \frac{-6}{2} = -3 \]

Since both pairs of points have the same slope of \(-3\), the table does represent a linear function.

Thus, the function is linear, and the slope is \[ \text{slope} = -3. \]