To find the slope \( m \) of the line defined by the points \((-6, -21)\) and \((8, -14)\), we can use the formula for the slope:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can assign the points as follows:
- \( (x_1, y_1) = (-6, -21) \)
- \( (x_2, y_2) = (8, -14) \)
Now we can plug the values into the slope formula:
\[ m = \frac{-14 - (-21)}{8 - (-6)} \]
This simplifies as follows:
\[ m = \frac{-14 + 21}{8 + 6} \] \[ m = \frac{7}{14} \] \[ m = \frac{1}{2} \]
Thus, the slope of the line is \(\frac{1}{2}\).