To find the slope of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula for slope \(m\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, the points are \((-1, 6)\) and \((14, 3)\). We can assign:
- \(x_1 = -1\)
- \(y_1 = 6\)
- \(x_2 = 14\)
- \(y_2 = 3\)
Now, we can plug these values into the slope formula:
\[ m = \frac{3 - 6}{14 - (-1)} \]
Calculating the numerator and the denominator:
\[ m = \frac{3 - 6}{14 + 1} = \frac{-3}{15} \]
Next, we simplify \(\frac{-3}{15}\):
\[ m = \frac{-1}{5} \]
Thus, the slope of the line that passes through the points \((-1, 6)\) and \((14, 3)\) is
\[ \boxed{-\frac{1}{5}} \]