Final answer:
The equation of the tangent line to the graph of f(x) = x at the point (16, 4) is y = x - 12.
Step-by-step explanation:
To find the equation of the tangent line to the graph of f(x) = x at the point (16, 4), we need to find the slope of the tangent line. The slope of the tangent line at a point on a graph is equal to the derivative of the function at that point. Since f(x) = x, the derivative is simply 1.
Using the point-slope form of a line, we can write the equation of the tangent line as y - y1 = m(x - x1), where (x1, y1) is the point of tangency and m is the slope of the tangent line. Plugging in the values, we get y - 4 = 1(x - 16), which simplifies to y - 4 = x - 16.
Therefore, the equation of the tangent line to the graph of f(x) = x at the point (16, 4) is y = x - 12.