Question

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

options:

−1 over 5

1 over 3

1

-3

Answer 1

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:

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