To determine the slope using the values given in the table, we will employ the formula for the slope between 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]
From the table, we can choose any pair of points to calculate the slope. However, we'll use the points [tex]\((x_1, y_1) = (-4, 19)\)[/tex] and [tex]\((x_2, y_2) = (4, 7)\)[/tex].
Now, we substitute these values into the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
[tex]\[
m = \frac{7 - 19}{4 - (-4)}
\][/tex]
[tex]\[
m = \frac{7 - 19}{4 + 4}
\][/tex]
[tex]\[
m = \frac{-12}{8}
\][/tex]
[tex]\[
m = -\frac{12}{8}
\][/tex]
Simplifying the fraction, we get:
[tex]\[
m = -\frac{3}{2}
\][/tex]
Therefore, the slope [tex]\(m\)[/tex] is:
[tex]\[
m = -\frac{3}{2}
\][/tex]
So, the correct answer is:
[tex]\[
-\frac{3}{2}
\][/tex]
