To find the value of \( g \) for the points \( (g, -1) \) and \( (2, 5) \) that lie on a line with a slope of \( \frac{3}{2} \), we can use the formula for the slope between two points, which is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the points \( (g, -1) \) as \( (x_1, y_1) \) and \( (2, 5) \) as \( (x_2, y_2) \):
\[ m = \frac{5 - (-1)}{2 - g} \]
Since the slope \( m \) is given as \( \frac{3}{2} \), we can set up the equation:
\[ \frac{5 + 1}{2 - g} = \frac{3}{2} \]
This simplifies to:
\[ \frac{6}{2 - g} = \frac{3}{2} \]
Next, we cross-multiply to solve for \( g \):
\[ 6 \cdot 2 = 3 \cdot (2 - g) \]
This simplifies to:
\[ 12 = 6 - 3g \]
Rearranging the equation to isolate \( g \):
\[ 12 - 6 = -3g \]
Simplifying further gives:
\[ 6 = -3g \]
Now, dividing both sides by -3:
\[ g = -2 \]
Thus, the value of \( g \) is
\[ \boxed{-2} \]