Question

Find an equation of the graph of the tangent line to the graph of y= g(x) at x = 2 if g(2) = -4 and g'(2) = 5. (enter your answer as an equation in terms of y and x)

Answer 1

y = mx + c represent equation of a line

at x = 2, g(x) = y = -4

-4 = 2m + c

at

g'(x) = m

g'(2) = 5

m = 5

substitute m in equation 1

-4 = 2 x 5 + c

-4 = 10 + c

c = -4 - 10

c = - 14

Equation of a line

y = 5x - 14