To find the slope of the line that passes through the points \((9, 9)\) and \((7, 12)\), we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can assign the coordinates as follows:
- \((x_1, y_1) = (9, 9)\)
- \((x_2, y_2) = (7, 12)\)
Now, substituting these values into the formula:
\[ m = \frac{12 - 9}{7 - 9} \]
Calculating the differences in the numerator and denominator:
\[ m = \frac{3}{-2} \]
Thus, the slope \(m\) is:
\[ m = -\frac{3}{2} \]
Therefore, the slope of the line that passes through the points \((9, 9)\) and \((7, 12)\) is \(\boxed{-\frac{3}{2}}\).
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