To find the slope of the line that passes through the points [tex]\((-1, -7)\)[/tex] and [tex]\((3, 9)\)[/tex], we'll follow these steps:
1. Identify the coordinates of the two points:
- Point 1: [tex]\((-1, -7)\)[/tex]
- Point 2: [tex]\((3, 9)\)[/tex]
2. Determine the change in y ([tex]\(\Delta y\)[/tex]) and the change in x ([tex]\(\Delta x\)[/tex]):
- [tex]\(\Delta y\)[/tex] is the difference in the y-coordinates:
[tex]\[
\Delta y = y_2 - y_1 = 9 - (-7) = 9 + 7 = 16
\][/tex]
- [tex]\(\Delta x\)[/tex] is the difference in the x-coordinates:
[tex]\[
\Delta x = x_2 - x_1 = 3 - (-1) = 3 + 1 = 4
\][/tex]
3. Calculate the slope (m) using the formula for the slope of a line through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
m = \frac{\Delta y}{\Delta x}
\][/tex]
Substituting the values of [tex]\(\Delta y\)[/tex] and [tex]\(\Delta x\)[/tex]:
[tex]\[
m = \frac{16}{4} = 4
\][/tex]
Therefore, the slope of the line through the points [tex]\((-1, -7)\)[/tex] and [tex]\((3, 9)\)[/tex] is 4. Thus, the correct answer is [tex]\( \boxed{4} \)[/tex].
