Question

Derive the slope of a line with the coordinates (−5,−2)
(
−
5
,
−
2
)
and (4,−8)
(
4
,
−
8
)

Answer 1

To find the slope of a line given two points, we can use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

In this case, the two points are \((-5, -2)\) and \((4, -8)\). We can assign:

\[
(x_1, y_1) = (-5, -2)
\]
\[
(x_2, y_2) = (4, -8)
\]

Now, let's substitute these coordinates into the formula:

1. Calculate \( y_2 - y_1 \):

\[
y_2 - y_1 = -8 - (-2) = -8 + 2 = -6
\]

2. Calculate \( x_2 - x_1 \):

\[
x_2 - x_1 = 4 - (-5) = 4 + 5 = 9
\]

3. Substitute these results into the slope formula:

\[
m = \frac{-6}{9}
\]

4. Simplify the fraction:

\[
m = -\frac{2}{3}
\]

Thus, the slope of the line connecting the points \((-5, -2)\) and \((4, -8)\) is

\[
\boxed{-\frac{2}{3}}
\]