Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = −5 and g'(4) = 6. (Enter your answer as an equation in terms of y and x.)

Answer 1

y=6x +29 is the equation of the tangent line when x= 4

(4,-5) is point on the graph and the tangent line

slope = 6 = m when x =4

y = mx +b is the general formula for the tangent line with m= slope, b=y intercept

plug in the point x=4, y=-5 and solve for b

-5 = 6(4) + b

b= -5-24 = -29

y = 6x -29

Answer 2

m = 6 at (4, -5)

Use point-slope form to determine equation.