Question

The table represents a linear function.

A two column table with six rows. The first row, x, has the entries negative 4, negative 2, negative 1, 1, 2. The second column, y, has the entries, negative 2, negative 10, negative 14, negative 22, negative 26.
What is the slope of the function?

–8
–4
2
5

Answer 1

To find the slope of the linear function represented by the table, we can use the formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Let's use two points from the table. We'll take the first pair of points: \((-4, -2)\) and \((-2, -10)\).

- \(x_1 = -4\), \(y_1 = -2\)
- \(x_2 = -2\), \(y_2 = -10\)

Now, plug these values into the slope formula:

\[
m = \frac{-10 - (-2)}{-2 - (-4)} = \frac{-10 + 2}{-2 + 4} = \frac{-8}{2} = -4
\]

Thus, the slope of the function is \(-4\).

The answer is \(-4\).