Answer:
11) D. y=5/2x+5/2
, 12) B. y=8/5x+69/5, 14) A. y=-9/5x-67/5
Step-by-step explanation:
11) The function of the perpendicular line can be found in terms of its slope and a given point by this formula:

Where:
,
- Components of the given point, dimensionless.
- Slope, dimensionless.
Besides, a slope that is perpendicular to original line can be calculated by this expression:

Where
is the slope of the original line, dimensionless.
The original slope is determined from the explicitive form of the given line:




The original slope is
, and the slope of the perpendicular line is:


If
,
and
, then:
![y-(-5) = \frac{5}{2}\cdot [x-(-3)]](https://tex.z-dn.net/?f=y-%28-5%29%20%3D%20%5Cfrac%7B5%7D%7B2%7D%5Ccdot%20%5Bx-%28-3%29%5D)


The right answer is D.
12) The function of the parallel line can be found in terms of its slope and a given point by this formula:

Where:
,
- Components of the given point, dimensionless.
- Slope, dimensionless.
Its slope is the slope of the given, which must be transformed into its explicitive form:



The slope of the parallel line is
.
If
,
and
, then:
![y-1 = \frac{8}{5}\cdot [x-(-8)]](https://tex.z-dn.net/?f=y-1%20%3D%20%5Cfrac%7B8%7D%7B5%7D%5Ccdot%20%5Bx-%28-8%29%5D)


The correct answer is B.
14) The function of the perpendicular line can be found in terms of its slope and a given point by this formula:

Where:
,
- Components of the given point, dimensionless.
- Slope, dimensionless.
Besides, a slope that is perpendicular to original line can be calculated by this expression:

Where
is the slope of the original line, dimensionless.
The original slope is determined from the explicitive form of the given line:



The original slope is
, and the slope of the perpendicular line is:



If
,
and
, then:
![y-1 = -\frac{9}{5}\cdot [x-(-8)]](https://tex.z-dn.net/?f=y-1%20%3D%20-%5Cfrac%7B9%7D%7B5%7D%5Ccdot%20%5Bx-%28-8%29%5D)


The correct answer is A.