To write an equation that represents the x-coordinates of the intersection points of two graphs, you need to set the equations of the two graphs equal to each other.

Let's say the graphs are represented by the equations:

1. $y = f(x)$
2. $y = g(x)$

The x-coordinates of the intersection points are the solutions to the equation:

$f(x) = g(x)$

This is the equation you are looking for, where the solutions provide the x-coordinates of the points where the two graphs intersect. If you provide specific functions for the graphs, I can help formulate a more specific equation.