Question

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

Answer 1

To find the slope of a line given two points, we can use the formula for the slope \( m \):

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

In your case, the coordinates of the two points are:
- Point 1: \( (-5, -2) \) (where \( x_1 = -5 \) and \( y_1 = -2 \))
- Point 2: \( (4, -8) \) (where \( x_2 = 4 \) and \( y_2 = -8 \))

Now, substituting these values into the slope formula:

\[
m = \frac{-8 - (-2)}{4 - (-5)}
\]

This simplifies to:

\[
m = \frac{-8 + 2}{4 + 5} = \frac{-6}{9}
\]

Now, simplifying \( -6/9 \):

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

Thus, the slope of the line that passes through the points \( (-5, -2) \) and \( (4, -8) \) is \( \boxed{-\frac{2}{3}} \).