To determine the slope of the line using the data points provided, we can use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \((-1, 6)\) and \((1, 9)\):
- Let \((x_1, y_1) = (-1, 6)\) and \((x_2, y_2) = (1, 9)\).
- Substitute these values into the slope formula:
\[ m = \frac{9 - 6}{1 - (-1)} = \frac{3}{2} = 1.5 \]
For confirmation, we can use another pair of points, \((1, 9)\) and \((3, 12)\):
- Let \((x_1, y_1) = (1, 9)\) and \((x_2, y_2) = (3, 12)\).
- Substitute these values into the slope formula:
\[ m = \frac{12 - 9}{3 - 1} = \frac{3}{2} = 1.5 \]
In both cases, the slope of the line is:
\[ \boxed{1.5} \]