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Find an equation of the tangent line to the graph of f at the given point. f(x) = x, (49, 7).

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Final answer:

To find the equation of the tangent line to the graph of f at the point (49, 7), we need to find the slope of the tangent line and use the point-slope form of a linear equation to derive the equation.

Step-by-step explanation:

1. Find the derivative of f(x) to find the slope of the tangent line. Since f(x) = x, its derivative is 1. This means that the slope of the tangent line is 1.

2. Use the point-slope form of a linear equation to find the equation of the tangent line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, the point on the line is (49, 7), and the slope is 1. Plugging in these values, we get y - 7 = 1(x - 49), which simplifies to y - 7 = x - 49.

3. Rewrite the equation in slope-intercept form to get the final equation of the tangent line. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation becomes y = x - 42. Therefore, the equation of the tangent line to the graph of f at the point (49, 7) is y = x - 42.

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