Question

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

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 \(m\):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Given the points \((-10, -1)\) 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:

\[
m = \frac{-4 - (-1)}{5 - (-10)}
\]

Simplifying this:

\[
m = \frac{-4 + 1}{5 + 10} = \frac{-3}{15}
\]

Now, simplify \(\frac{-3}{15}\):

\[
m = \frac{-1}{5}
\]

Thus, the slope of the line that passes through the points \((-10, -1)\) and \((5, -4)\) is \(\boxed{-\frac{1}{5}}\).