To find the midpoint of a line segment with endpoints \((-5, 4)\) and \((-3, 6)\), we can use the midpoint formula:
\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.
In this case:
- \((x_1, y_1) = (-5, 4)\)
- \((x_2, y_2) = (-3, 6)\)
Now substituting these values into the midpoint formula:
\[ \text{Midpoint} = \left( \frac{-5 + (-3)}{2}, \frac{4 + 6}{2} \right) \]
Calculating the x-coordinate:
\[ \frac{-5 - 3}{2} = \frac{-8}{2} = -4 \]
Calculating the y-coordinate:
\[ \frac{4 + 6}{2} = \frac{10}{2} = 5 \]
Thus, the midpoint of the line segment is:
\[ (-4, 5) \]
Therefore, the answer is \((-4, 5)\).