To find the slope [tex]\( m \)[/tex] of the linear function given the points (4, -1) and (-8, -2), you can use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the coordinates of the points into the formula:
- For the point (4, -1):
- [tex]\( x_1 = 4 \)[/tex]
- [tex]\( y_1 = -1 \)[/tex]
- For the point (-8, -2):
- [tex]\( x_2 = -8 \)[/tex]
- [tex]\( y_2 = -2 \)[/tex]
Now, substitute these values into the slope formula:
[tex]\[
m = \frac{-2 - (-1)}{-8 - 4} = \frac{-2 + 1}{-8 - 4} = \frac{-1}{-12} = \frac{1}{12}
\][/tex]
Therefore, the slope [tex]\( m \)[/tex] is:
[tex]\[
m = \frac{1}{12} \approx 0.0833333
\][/tex]
