To determine the slope of a linear function given by a set of points, you can use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, [tex]\(m\)[/tex] is the slope, and [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are any two points on the line.
Let's use the points [tex]\((-4, -2)\)[/tex] and [tex]\((-2, -10)\)[/tex] from the table:
Step-by-Step Solution:
1. Identify the coordinates of the two points.
[tex]\[
(x_1, y_1) = (-4, -2)
\][/tex]
[tex]\[
(x_2, y_2) = (-2, -10)
\][/tex]
2. Substitute these coordinates into the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
3. Perform the substitution:
[tex]\[
m = \frac{-10 - (-2)}{-2 - (-4)}
\][/tex]
4. Simplify inside the parentheses:
[tex]\[
m = \frac{-10 + 2}{-2 + 4}
\][/tex]
[tex]\[
m = \frac{-8}{2}
\][/tex]
5. Divide to get the slope:
[tex]\[
m = -4
\][/tex]
Thus, the slope of the function is [tex]\(-4\)[/tex].
