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Find an equation of the tangent line to the graph of f at the given point. f(x) = x, (9, 3)

User Dariush
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Final answer:

The equation of the tangent line to the graph of f at the given point is y = x - 6.

Step-by-step explanation:

The equation of the tangent line to the graph of f at the given point can be found using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope of the tangent line is equal to the slope of the function f at the given point. The slope of f(x) = x is always 1, so the slope of the tangent line is also 1. The y-intercept of the tangent line can be found by substituting the x-coordinate of the given point (9) and the y-coordinate of the given point (3) into the equation.

Using the formula, y = mx + b, we have:

3 = 1 * 9 + b

3 = 9 + b

b = 3 - 9

b = -6

So the equation of the tangent line is y = x - 6.

User Nrussell
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