To find the slope of the line passing through the points \((-4, 6)\) and \( (3, -8) \), we use the slope formula, which is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points. In this problem:
- \( x_1 = -4 \)
- \( y_1 = 6 \)
- \( x_2 = 3 \)
- \( y_2 = -8 \)
Substituting these coordinates into the slope formula, we get:
[tex]\[ m = \frac{-8 - 6}{3 - (-4)} \][/tex]
Simplify the numerator and denominator step-by-step:
### Numerator:
[tex]\[ -8 - 6 = -14 \][/tex]
### Denominator:
[tex]\[ 3 - (-4) = 3 + 4 = 7 \][/tex]
Now, substitute these simplified values back into the slope formula:
[tex]\[ m = \frac{-14}{7} \][/tex]
Finally, simplify the fraction:
[tex]\[ m = -2 \][/tex]
Thus, the slope of the line passing through the points [tex]\((-4, 6)\)[/tex] and [tex]\((3, -8)\)[/tex] is [tex]\(-2.0\)[/tex].
