Question

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

Answer 1

To find the equation of the tangent line to the graph of y = g(x) at x = 6, use the derivative of g(x) and the given point and slope.

Step-by-step explanation:

To find the equation of the tangent line to the graph of y = g(x) at x = 6, we need to use the derivative of g(x).

Given that g(6) = -4 and g'(6) = 5, we know that the point (6, -4) is on the graph and the slope of the tangent line is 5.

Using the point-slope form of a linear equation, the equation of the tangent line is y - (-4) = 5(x - 6), which simplifies to y = 5x - 34. This is the equation of the tangent line to the graph of y = g(x) at x = 6.