Final answer:
To find the equation of the tangent line to the graph of y = g(x) at x = 4, we use the values of g(4) and g'(4). The slope of the tangent line is the derivative of the function at x = 4, which is g'(4). The equation of the tangent line 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 values of g(4) and g'(4). Given that g(4) = -6 and g'(4) = 2, we can determine the slope of the tangent line. The slope of the tangent line is equal to the derivative of the function at x = 4, which is g'(4). So, the slope of the tangent line is 2.
Now, we can use the point-slope form of a linear equation to write the equation of the tangent line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. We know that the point (4, -6) lies on the tangent line and the slope of the tangent line is 2. Plugging in these values, we get the equation y - (-6) = 2(x - 4).
Simplifying this equation gives y + 6 = 2x - 8. Rearranging the equation, we get y = 2x - 14. Therefore, the equation of the tangent line to the graph of y = g(x) at x = 4 is y = 2x - 14.