Question

If the instantaneous rate of change of f(x) at (2,-4) is 5, write the equation of the line tangent to the graph of f(x) at x=2.

Answer 1

slope = 5 at x = 2 so
y = 5 x + b
-4 = 5 (2) + b
-4 = 10 + b
b = -14
so
y = 5 x -14

Answer 2

you have a point and a slope, so just use the point-slope form, which you learned in Algebra I:

y+4 = 5(x-2)