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For the function f(x)=-6x-9, find the slope of the tangent line at x=1. Answer:

For the function f(x)=−6x−9 f(x)=-6 x-9 , find the slope of the tangent line at x=1 x=1 .\newlineAnswer:

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Q. For the function f(x)=−6x−9 f(x)=-6 x-9 , find the slope of the tangent line at x=1 x=1 .\newlineAnswer:
  1. Identify Function Type: Identify the type of function and the method to find the slope of the tangent line.\newlineThe function f(x)=−6x−9f(x) = -6x - 9 is a linear function. The slope of the tangent line to a linear function is the same as the slope of the function itself.
  2. Determine Slope: Determine the slope of the function.\newlineFor a linear function in the form y=mx+by = mx + b, the slope is the coefficient of xx, which is mm. In the function f(x)=−6x−9f(x) = -6x - 9, the coefficient of xx is −6-6.
  3. Conclude Tangent Slope: Conclude the slope of the tangent line at x=1x = 1. Since the slope of the function is constant, the slope of the tangent line at any point, including x=1x = 1, is −6-6.

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