Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = −3 and g'(6) = 5. (Enter your answer as an equation in terms of y and x.)

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FelisFelis FelisFelis · Answer 1 · 2019-07-04T13:16:09+02:00

Answer:

The equation of tangent line is [tex]y=5x-33 [/tex]

Step-by-step explanation:

We need to find out the equation of tangent line.

Given :- g(6)=−3 and g'(6)= 5

If g(6)=−3

then the point on the line for the required tangent is (6,−3)

If g'(6)= 5

then the slope of the tangent at that point is 45

The tangent line can be specified by the slope-point form of the equation:

[tex](y-y_1)=m(x-x_1)[/tex]

which in this case is

[tex](y-(-3))=5(x-6)[/tex]

[tex](y+3)=(5x-30)[/tex]

subtract both the sides by 3,

[tex]y+3-3=5x-30-3[/tex]

[tex]y=5x-33[/tex]

Therefore, the equation of tangent line is [tex]y=5x-33[/tex]