To determine the slope of the linear function represented by the table, we must calculate the rate of change between two points on the line. The slope [tex]\( m \)[/tex] of a linear function can be found using the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
We'll use the first two points [tex]\((-2, 8)\)[/tex] and [tex]\((-1, 2)\)[/tex] from the table to find the slope.
1. Identify the coordinates of the first point [tex]\((x_1, y_1)\)[/tex]:
[tex]\[
x_1 = -2, \quad y_1 = 8
\][/tex]
2. Identify the coordinates of the second point [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
x_2 = -1, \quad y_2 = 2
\][/tex]
3. Substitute these values into the slope formula:
[tex]\[
m = \frac{2 - 8}{-1 - (-2)}
\][/tex]
4. Simplify the numerator and the denominator:
[tex]\[
m = \frac{-6}{1}
\][/tex]
5. Calculate the slope:
[tex]\[
m = -6
\][/tex]
Therefore, the slope of the function is [tex]\( -6 \)[/tex].
From the provided options, [tex]\( -6 \)[/tex], [tex]\( -4 \)[/tex], [tex]\( 4 \)[/tex], and [tex]\( 6 \)[/tex], the correct slope of the linear function is [tex]\( -6 \)[/tex].
