The formula for finding the midpoint of a segment between two points $R(x_1, y_1)$ and $S(x_2, y_2)$ is given by:

$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

For the points $R(1, -1)$ and $S(6, 4)$, we can substitute their coordinates into the formula:

$\text{Midpoint} = \left( \frac{1 + 6}{2}, \frac{-1 + 4}{2} \right) = \left( \frac{7}{2}, \frac{3}{2} \right)$

Now, sum the $x$- and $y$-coordinates of the midpoint:

$x + y = \frac{7}{2} + \frac{3}{2} = \frac{10}{2} = 5$

Thus, the value of $x + y$ is $5$.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How can we verify the calculation of the midpoint for any line segment?
2. What is the distance between points $R(1, -1)$ and $S(6, 4)$?
3. How can you find the equation of the line passing through points $R(1, -1)$ and $S(6, 4)$?
4. What is the slope of the line segment connecting points $R(1, -1)$ and $S(6, 4)$?
5. How would you find the midpoint if one of the points was at the origin?

Tip: The midpoint formula always provides the average of the coordinates of the two points.