Find the equation of the tangent line to y=e^(-7t) at t=0

Question

Find the equation of the tangent line to y=e^(-7t) at t=0

Answer 1

y=e^(-7t)

y' = -7e^-7t

y'(0) = -7e^-7(0)

y'(0) = -7(1)

y-(0) = -7

the tangent line goes through the point (0,1) with slope =-7

-7 = (y-1)/(x-0) in point slope form

y= -7x +1 is the tangent line in slope intercept form, when t=0