Final answer:
To find the equation of the tangent line to the graph of y = g(x) at x = 2, we need to use the point-slope form of a linear equation. Given that g(2) = -4 and g'(2) = 6, the equation of the tangent line is y = 6x - 16.
Step-by-step explanation:
To find the equation of the tangent line to the graph of y = g(x) at x = 2, we need to use the point-slope form of a linear equation. The formula for the point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Given that g(2) = -4 and g'(2) = 6, we know that the point (2, -4) lies on the graph of y = g(x) and the slope of the tangent line at x = 2 is 6.
Therefore, the equation of the tangent line is y - (-4) = 6(x - 2), which simplifies to y + 4 = 6x - 12. By rearranging the equation, we get the final equation of the tangent line as y = 6x - 16.