Find the slope of a line that passes through (-10, -1) and (5, -4).

options:

−1 over 5

1 over 3

1

-3

1 answer

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:

  1. Numerator: \(-4 - (-1) = -4 + 1 = -3\)

  2. 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:

\(-1 \text{ over } 5\)