To determine the slope of the line passing through the points [tex]\((-1, 4)\)[/tex] and [tex]\((14, -2)\)[/tex], we use the formula for the slope [tex]\( m \)[/tex] which is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, [tex]\((x_1, y_1) = (-1, 4)\)[/tex] and [tex]\((x_2, y_2) = (14, -2)\)[/tex].
1. Calculate the difference in the y-coordinates (the rise):
[tex]\[ y_2 - y_1 = -2 - 4 = -6 \][/tex]
2. Calculate the difference in the x-coordinates (the run):
[tex]\[ x_2 - x_1 = 14 - (-1) = 14 + 1 = 15 \][/tex]
3. Substitute these values into the slope formula:
[tex]\[ m = \frac{-6}{15} \][/tex]
4. Simplify the fraction:
[tex]\[ m = -\frac{6}{15} \][/tex]
Therefore, the slope of the line that goes through the points [tex]\((-1, 4)\)[/tex] and [tex]\((14, -2)\)[/tex] is [tex]\(-\frac{6}{15}\)[/tex].
Thus, the correct answer is:
D. [tex]\(-\frac{6}{15}\)[/tex]
