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

(

5
,

2
)
and (4,−8)
(
4
,

8
)

1 answer

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 \( y_2 - y_1 \):

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

  1. Calculate \( x_2 - x_1 \):

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

  1. Substitute these results into the slope formula:

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

  1. Simplify the fraction:

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

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

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