To find the slope of the line that contains the points [tex]\((-2, 7)\)[/tex] and [tex]\( (2, 3) \)[/tex], we can use the slope formula, which is given by:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of the first point, and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the second point. Substituting the coordinates given in the question:
- For the first point [tex]\((-2, 7)\)[/tex], we have [tex]\(x_1 = -2\)[/tex] and [tex]\(y_1 = 7\)[/tex].
- For the second point [tex]\((2, 3)\)[/tex], we have [tex]\(x_2 = 2\)[/tex] and [tex]\(y_2 = 3\)[/tex].
Now, substitute these values into the slope formula:
[tex]\[
\text{slope} = \frac{3 - 7}{2 - (-2)}
\][/tex]
Next, simplify the numerator and the denominator:
[tex]\[
\text{slope} = \frac{3 - 7}{2 + 2} = \frac{-4}{4}
\][/tex]
Finally, compute the division:
[tex]\[
\text{slope} = -1
\][/tex]
Therefore, the slope of the line that contains the points [tex]\((-2, 7)\)[/tex] and [tex]\( (2, 3) \)[/tex] is [tex]\(-1\)[/tex].
Hence, the correct answer is:
B. -1
