To determine the slope of the linear function represented by the table, we need to use the slope formula which is calculated as the change in y divided by the change in x. This formula is written as:
[tex]\[
\text{slope} = \frac{\Delta y}{\Delta x}
\][/tex]
where \(\Delta y\) represents the change in the y-values, and \(\Delta x\) represents the change in the x-values.
Let's take the first two points from the table to find the slope:
The points are:
[tex]\[
(x_1, y_1) = (-2, 8)
\][/tex]
[tex]\[
(x_2, y_2) = (-1, 2)
\][/tex]
Now, calculate the change in y (\(\Delta y\)) and the change in x (\(\Delta x\)):
[tex]\[
\Delta y = y_2 - y_1 = 2 - 8 = -6
\][/tex]
[tex]\[
\Delta x = x_2 - x_1 = -1 - (-2) = -1 + 2 = 1
\][/tex]
Next, we substitute these values into the slope formula:
[tex]\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{-6}{1} = -6.0
\][/tex]
Therefore, the slope of the function is:
[tex]\[
-6.0
\][/tex]
So, the correct option is:
[tex]\[
-6
\][/tex]
