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.)

Accepted Solution

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)=  5If  g(6)=−3then the point on the line for the required tangent is  (6,−3)If  g'(6)=  5then the slope of the tangent at that point is  45The 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]