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 the slope \(m\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, the points are \((-10, -1)\) and \((5, -4)\). We can assign:
- \(x_1 = -10\), \(y_1 = -1\)
- \(x_2 = 5\), \(y_2 = -4\)
Now we can substitute these values into the slope formula:
\[ m = \frac{-4 - (-1)}{5 - (-10)} \]
Calculating the numerator and the denominator separately:
-
Numerator: \(-4 - (-1) = -4 + 1 = -3\)
-
Denominator: \(5 - (-10) = 5 + 10 = 15\)
Now substituting back into the slope formula gives us:
\[ m = \frac{-3}{15} \]
This simplifies to:
\[ m = \frac{-1}{5} \]
Thus, the slope of the line that passes through the points \((-10, -1)\) and \((5, -4)\) is:
\(-\frac{1}{5}\)
Therefore, the correct answer is:
\(-1 \text{ over } 5\)