Question

The table represents a linear function.

A two column table with six rows. The first column, x, has the entries, negative 2, negative 1, 0, 1, 2. The second column, y, has the entries, negative 8, 2, negative 4, negative 10, negative 16.
What is the slope of the function?

–6
–4
4
6

Answer 1

To determine the slope of the linear function represented by the table, we need to pick two points from the table and use the slope formula:

\[ \text{slope} (m) = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]

We can pick any two points from the table. Let's use the points \((x_1, y_1) = (-2, -8)\) and \((x_2, y_2) = (-1, -2)\).

Substitute the values into the slope formula:

\[ m = \frac{-2 - (-8)}{-1 - (-2)} \]
\[ m = \frac{-2 + 8}{-1 + 2} \]
\[ m = \frac{6}{1} \]
\[ m = 6 \]

So, the slope of the function is 6.