To determine the slope of the line that passes through the points [tex]\((2, -7)\)[/tex] and [tex]\((-1, 5)\)[/tex], we use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\((x_1, y_1) = (2, -7)\)[/tex] and [tex]\((x_2, y_2) = (-1, 5)\)[/tex]. Plugging in the coordinates of the points, we get:
[tex]\[
m = \frac{5 - (-7)}{-1 - 2}
\][/tex]
First, simplify the numerator:
[tex]\[
5 - (-7) = 5 + 7 = 12
\][/tex]
Next, simplify the denominator:
[tex]\[
-1 - 2 = -3
\][/tex]
Now, divide the numerator by the denominator:
[tex]\[
m = \frac{12}{-3} = -4
\][/tex]
Therefore, the slope of the line that contains the points [tex]\((2, -7)\)[/tex] and [tex]\((-1, 5)\)[/tex] is [tex]\(-4\)[/tex].
So the correct answer is:
[tex]\[
-4
\][/tex]
