To find the slope of a line that goes through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
For the points \((4, 7)\) and \((-1, 9)\):
- \(x_1 = 4\), \(y_1 = 7\)
- \(x_2 = -1\), \(y_2 = 9\)
Now, substituting into the slope formula:
\[ m = \frac{9 - 7}{-1 - 4} \] \[ m = \frac{2}{-5} \] \[ m = -\frac{2}{5} \]
Thus, the slope of the line is \(-\frac{2}{5}\).