Find an equation of the tangent line to the graph of  y = g(x) at x = 6 if g(6) = −3 and g'(6) = 2.  

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You need to remember the form of equation of tangent line to the graph of function at a point `x=a`  such that:

`g(x)- g(a) = g'(a)(x-a)`

Notice that the problem does not provide the equation of function, but it provides the values of `g(x) ` and `g'(x)`  at `x =6` ...

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You need to remember the form of equation of tangent line to the graph of function at a point `x=a`  such that:

`g(x)- g(a) = g'(a)(x-a)`

Notice that the problem does not provide the equation of function, but it provides the values of `g(x) ` and `g'(x)`  at `x =6`  such that:

`g(x) - g(6) = g'(6)(x-6)`

Substituting -3 for `g(6)`  and 2 for `g'(6)`  yields:

`g(x) -(-3) = 2(x-6) => g(x) + 3 = 2x - 12`

Substituting y for g(x) yields:

`y = 2x - 12 - 3 => y = 2x - 15`

Hence, evaluating the equation of the tangent line to the graph of the function g(x), at x = 6, yields `y = 2x - 15.`

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