To find the slope of the line that passes through the points [tex]\((-1, 4)\)[/tex] and [tex]\( (14, -2) \)[/tex], we use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where [tex]\( (x_1, y_1) = (-1, 4) \)[/tex] and [tex]\( (x_2, y_2) = (14, -2) \)[/tex].
First, calculate the difference in the y-coordinates (the numerator):
[tex]\[ y_2 - y_1 = -2 - 4 = -6 \][/tex]
Next, calculate the difference in the x-coordinates (the denominator):
[tex]\[ x_2 - x_1 = 14 - (-1) = 14 + 1 = 15 \][/tex]
Now, substitute these values into the slope formula:
[tex]\[ m = \frac{-6}{15} \][/tex]
To simplify [tex]\(\frac{-6}{15}\)[/tex], we divide both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[ \frac{-6}{15} = \frac{-6 \div 3}{15 \div 3} = \frac{-2}{5} \][/tex]
Thus, the slope of the line is:
[tex]\[ \boxed{-\frac{2}{5}} \][/tex]
None of the given options matches [tex]\(-\frac{2}{5}\)[/tex], but if we need to select the closest match among the provided choices, the closest equivalent fraction is:
[tex]\[ D. -\frac{6}{15} \][/tex]
Since [tex]\(\frac{-2}{5}\)[/tex] is equivalent to [tex]\(\frac{-6}{15}\)[/tex], the correct answer is:
[tex]\[ \boxed{D} \][/tex]
