Question

Find an equation of the tangent line to the graph of

y = g(x) at x = 5 if g(5) = -3 and g'(5) = 2.

Answer 1

To find the equation of the tangent line to the graph of y = g(x) at x = 5, use the point-slope form with 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 = 5, we need to use the point-slope form of a 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 of the line. In this case, we are given that g(5) = -3 and g'(5) = 2.

First, we know that the point (5, -3) is on the tangent line. Next, we know that the slope of the tangent line is given by g'(5). So, we can plug in the values into the point-slope form and simplify:

y - (-3) = 2(x - 5)

y + 3 = 2x - 10

y = 2x - 13

Therefore, the equation of the tangent line to the graph of y = g(x) at x = 5 is y = 2x - 13.