Final answer:
The equation of the line tangent to the graph of G(x) = 4e - 6x at the point (0,4) is y = -6x + 4.
Step-by-step explanation:
To find the equation of the line tangent to the graph of G(x) = 4e - 6x at the point (0,4), we need to find the derivative of G(x) and evaluate it at x = 0. The derivative of 4e - 6x is -6. This represents the slope of the tangent line. The equation of a line in point-slope form is y - y1 = m(x - x1), so plugging in the values y1 = 4, x1 = 0, and m = -6, we get the equation y - 4 = -6(x - 0), which simplifies to y = -6x + 4.