To determine the slope [tex]\(m\)[/tex] from the given table of points, we can use the formula for the slope of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Let's select the first two points from the table to find the slope. These points are:
[tex]\[
(x_1, y_1) = (-4, 19)
\][/tex]
[tex]\[
(x_2, y_2) = (-2, 16)
\][/tex]
Substitute these values into the slope formula:
[tex]\[
m = \frac{16 - 19}{-2 - (-4)}
\][/tex]
Simplify the numerator and the denominator separately:
[tex]\[
16 - 19 = -3
\][/tex]
[tex]\[
-2 - (-4) = -2 + 4 = 2
\][/tex]
Thus, the slope is:
[tex]\[
m = \frac{-3}{2}
\][/tex]
So, the correct value of the slope is:
[tex]\[
-\frac{3}{2}
\][/tex]
