Final answer:
The equation of the tangent line to the function f(x) = x at the point (25, 5) is found using the slope of 1 at that point and the point-slope form, resulting in the equation y = x - 20.
Step-by-step explanation:
The question is asking to find the equation of the tangent line to the graph of the function f(x) = x at the specified point (25, 5). To do this, we use the fact that the slope of the curve at a specific point is equal to the slope of the tangent line at that point.
To find the slope of the function f(x) = x, we differentiate it with respect to x. Since the derivative of x with respect to x is 1, the slope of the tangent line is also 1. Knowing the slope and the point through which the tangent line passes, we can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point on the tangent line and m is the slope.
Using the given point (25, 5) and the calculated slope, the equation of the tangent line is y - 5 = 1(x - 25) or y = x - 20.