Question

Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -6 and g'(4) = 2. 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 = 4 is y = 2x - 14.

Step-by-step explanation:

To find the equation of the tangent line to the graph of y = g(x) at x = 4, we need to use the point-slope form of the equation of a line, which is y - y1 = m(x - x1).

Given g(4) = -6 and g'(4) = 2, we have the point (4, -6) and the slope m = 2.

Plugging these values into the point-slope form, we get y - (-6) = 2(x - 4), which simplifies to y + 6 = 2x - 8.

Therefore, the equation of the tangent line is y = 2x - 14.