To find the slope of a secant line, we need to find the difference in y-coordinates divided by the difference in x-coordinates between two points on the graph.

Let’s choose two points on the graph of G(x)=x^3-4x+6: (1,2) and another point (x, y) on the graph.

The slope of the secant line is given by:

slope = (change in y-coordinates) / (change in x-coordinates)

= (y - 2) / (x - 1)

Now, let’s substitute the function G(x) into the equation:

slope = (G(x) - 2) / (x - 1)

= ((x^3 - 4x + 6) - 2) / (x - 1)

= (x^3 - 4x + 4) / (x - 1)

Therefore, the slope of the secant line to the graph of G(x)=x^3-4x+6 over the interval (1, x) is (x^3 - 4x + 4) / (x - 1).