Given that the line $y=mx+k$ intersects the parabola $y=ax^2+bx+c$ at two points, compute the product of the two $x$-coordinates of these points in terms of $a$, $b$, $c$, $k$, and $m$.
1. To find the points of intersection between the line \( y = mx + k \) and the parabola \( y = ax^2 + bx + c \), we set the equations equal to each other:
   \[
   mx + k = ax^2 + bx + c
   \]
2. Rearrange the equation to form a standard quadratic equation:
   \[
   ax^2 + (b - m)x + (c - k) = 0
   \]
3. Let the roots of this quadratic equation be \( x_1 \) and \( x_2 \). According to Vieta's formulas, the product of the roots of the quadratic equation \( ax^2 + bx + c = 0 \) is given by:
   \[
   x_1 x_2 = \frac{c}{a}
   \]
   For our specific quadratic equation \( ax^2 + (b - m)x + (c - k) = 0 \), the product of the roots \( x_1 \) and \( x_2 \) is:
   \[
   x_1 x_2 = \frac{c - k}{a}
   \]

The final answer is \(\boxed{\frac{c - k}{a}}\)