Answer:
a) (i)
, (ii)
, (iii)
, (iv)
, (v)
, (vi)
, (vii)
, (viii)
; b)
; c) The equation of the tangent line to curve at P (7, -2) is
.
Step-by-step explanation:
a) The slope of the secant line PQ is represented by the following definition of slope:

(i)
:




(ii) 




(iii) 




(iv) 




(v) 




(vi) 




(vii) 




(viii) 




b) The slope at P (7,-2) can be estimated by using the following average:



The slope of the tangent line to the curve at P(7, -2) is 2.
c) The equation of the tangent line is a first-order polynomial with the following characteristics:

Where:
- Independent variable.
- Depedent variable.
- Slope.
- x-Intercept.
The slope was found in point (b) (m = 2). Besides, the point of tangency (7,-2) is known and value of x-Intercept can be obtained after clearing the respective variable:



The equation of the tangent line to curve at P (7, -2) is
.