To determine the slope of the linear function represented by the given points, follow these steps:
1. Select any two consecutive data points from the table to use for calculations. In this case, let's use the points [tex]\((-2, 8)\)[/tex] and [tex]\((-1, 2)\)[/tex].
2. Calculate the change in [tex]\( y \)[/tex] (often referred to as [tex]\(\Delta y\)[/tex] or "delta y") between these two points:
[tex]\[
\Delta y = y_2 - y_1 = 2 - 8 = -6
\][/tex]
3. Calculate the change in [tex]\( x \)[/tex] (often referred to as [tex]\(\Delta x\)[/tex] or "delta x") between these two points:
[tex]\[
\Delta x = x_2 - x_1 = -1 - (-2) = -1 + 2 = 1
\][/tex]
4. Finally, determine the slope ([tex]\(m\)[/tex]) of the function using the formula:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{-6}{1} = -6
\][/tex]
Based on these calculations, the slope (m) of the linear function is [tex]\(-6\)[/tex].
Therefore, the answer is:
[tex]\[ -6 \][/tex]
