Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = −6 and g'(3) = 2. (Enter your answer as an equation in terms of y and x.)

Answer 1

you will use the equation y = mx+b to graph this line.

since the first derivative is the slope at that point, the slope of the line tangent to this graph at 3 is equal to 2

y = 2x+b

you have an x and y coordinate at this point so you can substitute 3, -6 in for X and Y to this equation and then solve for b

-6 = 2(3)+b

subtract 6 from both sides

-12= b

y = 2x-12