Question

Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = -2 and g'(5) = 6. Enter your answer as an equation in terms of y and x.

Answer 1

The equation of the tangent line to the graph of y = g(x) at x = 5 is y = 6x - 32.

Step-by-step explanation:

The equation of the tangent line to the graph of y = g(x) at x = 5 can be found using the point-slope form of a line. The slope of the tangent line is equal to g'(5), which is given as 6. The point (5, g(5)) lies on the tangent line, so the equation of the tangent line is y - g(5) = g'(5)(x - 5). Substituting the values g(5) = -2 and g'(5) = 6, we get the equation y + 2 = 6(x - 5), which can be simplified to y = 6x - 32.