To find the slope of a line that contains two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], you can use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given the points [tex]\((-2, 7)\)[/tex] and [tex]\((2, 3)\)[/tex], we can identify [tex]\(x_1 = -2\)[/tex], [tex]\(y_1 = 7\)[/tex], [tex]\(x_2 = 2\)[/tex], and [tex]\(y_2 = 3\)[/tex].
Step-by-step, the formula is applied as follows:
1. Subtract the [tex]\(y\)[/tex]-coordinates: [tex]\( y_2 - y_1 = 3 - 7 = -4 \)[/tex].
2. Subtract the [tex]\(x\)[/tex]-coordinates: [tex]\( x_2 - x_1 = 2 - (-2) = 2 + 2 = 4 \)[/tex].
3. Divide the difference of the [tex]\(y\)[/tex]-coordinates by the difference of the [tex]\(x\)[/tex]-coordinates:
[tex]\[ m = \frac{-4}{4} = -1 \][/tex]
Therefore, the slope of the line that contains the points [tex]\((-2, 7)\)[/tex] and [tex]\((2, 3)\)[/tex] is [tex]\(-1.0\)[/tex].
The correct answer is:
A. [tex]\(-1\)[/tex]
