To determine the slope of the line that contains the points [tex]\((-1, -1)\)[/tex] and [tex]\((3, 15)\)[/tex], we can use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of the first point [tex]\((-1, -1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the second point [tex]\((3, 15)\)[/tex].
Step-by-step solution:
1. Identify the coordinates of the given points:
[tex]\[
x_1 = -1, \quad y_1 = -1, \quad x_2 = 3, \quad y_2 = 15
\][/tex]
2. Substitute these values into the slope formula:
[tex]\[
m = \frac{15 - (-1)}{3 - (-1)}
\][/tex]
3. Simplify the expression:
[tex]\[
m = \frac{15 + 1}{3 + 1}
\][/tex]
4. Perform the arithmetic operations:
[tex]\[
m = \frac{16}{4}
\][/tex]
5. Simplify the fraction:
[tex]\[
m = 4
\][/tex]
Therefore, the slope of the line containing the points [tex]\((-1, -1)\)[/tex] and [tex]\((3, 15)\)[/tex] is [tex]\(\boxed{4}\)[/tex]. This corresponds to option D.
