Find the equation of the tangent line...?

Question

Y = x^5

1)Find the slope of the tangent line to the curve at the point (-1, -1). The slope is?

--> I was able to get 5, which is correct

2) Find the equation of the tangent line in part 1.The tangent line is y =

--> I am having difficulty with this part.

Answer 1

y = x^5

slope of the tangent line, m = y'

y'(x) = 5 x^4

m = y'(-1) = 5(-1)^4 = 5

let the equation of tangent line

y-y1 = m(x-x1), where (x1=-1, y1 = -1 and m =5)

y + 1 = 5(x+1)

y+1 = 5x+5

y - 5x = 4

Answer 2

You know the slope is 5, so the equation of the tangent is of the form

y = 5x + b

You also know that (-1, -1) is a point on the ljne, so
-1 = 5(-1) + b
-1 = -5 + b
b = -1 - (-5)
b = 4

so the equation of the tangent line is:
y = 5x + 4

Answer 3

y = x^5
y ' = 5 x^4 . . . . . . substitute (-1, -1)
y ' = 5 (-1)^4 = 5
slope = 5 = (y +1) / (x + 1)
5 (x + 1) = ( y + 1)
5x + 5 = y + 1
5x - y + 4 = 0

y ' = 5 x^4
1 = 5 x^4
x^4 = 1/5 = 0.2
x = 0.66874 . . . . . solving next value of y
y = x^5 = 0.66874^5 = 0.13375
slope =1 = (y - 0.13375 ) / (x - 0.66874)

(y - 0.13375 ) = (x - 0.66874)
y - x = 0.535 . . . . . . this is the final equation