Find Equations of the Tangent Lines to the Curve $y = \frac { x - 8 } { x + 8 }$

question 59

Essay

Find equations of the tangent lines to the curve $y = \frac { x - 8 } { x + 8 }$ that are parallel to the line $x - y = 8 .$
A) $x - y = - 18.5$
B) $x - y = - 4.5$
C) $x - y = - 1.5$
D) $x - y = - 12.5$
E) $x - y = - 15$

• A) \(x - y = - 18.5\)
• B) \(x - y = - 4.5\)
• C) \(x - y = - 1.5\)
• D) \(x - y = - 12.5\)
• E) \(x - y = - 15\)

---

Definitions:

Arctic Winds

Cold, often powerful winds originating from the Arctic regions, affecting climate and weather patterns.

Montane Successional Gradient

The sequence of community changes which occur on a mountain over time, from pioneer species to a stable climax community.

Eutrophication

An increase in the concentration of chemical nutrients in an ecosystem to an extent that increases the growth of algae and higher plants, often resulting in the depletion of oxygen.

Conifers

A group of cone-bearing seed plants, mostly evergreens, that include pines, spruces, and firs, known for their needle-like or scale-like leaves.