To determine the slope of the line passing through the points [tex]\((-2, 7)\)[/tex] and [tex]\((2, 3)\)[/tex], we use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Where [tex]\((x_1, y_1)\)[/tex] is the first point and [tex]\((x_2, y_2)\)[/tex] is the second point.
Given:
[tex]\[
(x_1, y_1) = (-2, 7) \\
(x_2, y_2) = (2, 3)
\][/tex]
Substitute these coordinates into the slope formula:
[tex]\[
m = \frac{3 - 7}{2 - (-2)}
\][/tex]
First, calculate the numerator:
[tex]\[
3 - 7 = -4
\][/tex]
Next, calculate the denominator:
[tex]\[
2 - (-2) = 2 + 2 = 4
\][/tex]
Now, substitute the values back into the formula:
[tex]\[
m = \frac{-4}{4} = -1
\][/tex]
Thus, the slope of the line that contains the points [tex]\((-2, 7)\)[/tex] and [tex]\((2, 3)\)[/tex] is:
[tex]\[
m = -1
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{-1}
\][/tex]
