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11. Through (-3,-5), perpendicular to -2x - 5y = -19

A. y=2/5x+2/5 B. y=3/5x-19/5 C. y=-5/2x+5/2 D. y=5/2x+5/2


12. Through (-8,1), parallel to -8x + 5y = 89

A. y=-8/5x-69/5 B. y=8/5x+69/5 C. y=8/5x-89/5 B. 5/8x-1/8


14. Through (-8,1), perpendicular to -5x + 9y = 49

A. y=-9/5x-67/5 B. y=-9/5x C. y=-5/9x-67 D.y=9/5x+67/5

User Nick Sinas
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1 Answer

3 votes

Answer:

11) D. y=5/2x+5/2 , 12) B. y=8/5x+69/5, 14) A. y=-9/5x-67/5

Explanation:

11) The function of the perpendicular line can be found in terms of its slope and a given point by this formula:


y-y_(o) = m_(\perp)\cdot (x-x_(o))

Where:


x_(o),
y_(o) - Components of the given point, dimensionless.


m_(\perp) - Slope, dimensionless.

Besides, a slope that is perpendicular to original line can be calculated by this expression:


m_(\perp) = -(1)/(m)

Where
m is the slope of the original line, dimensionless.

The original slope is determined from the explicitive form of the given line:


-2\cdot x - 5\cdot y = -19


2\cdot x +5\cdot y = 19


5\cdot y = 19 - 2\cdot x


y = (19)/(5) -(2)/(5)\cdot x

The original slope is
-(2)/(5), and the slope of the perpendicular line is:


m_(\perp) = -(1)/(\left(-(2)/(5)\right) )


m_(\perp) = (5)/(2)

If
x_(o) = -3,
y_(o) = -5 and
m_(\perp) = (5)/(2), then:


y-(-5) = (5)/(2)\cdot [x-(-3)]


y + 5 = (5)/(2)\cdot x +(15)/(2)


y = (5)/(2)\cdot x +(5)/(2)

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:


y-y_(o) = m_(\parallel)\cdot (x-x_(o))

Where:


x_(o),
y_(o) - Components of the given point, dimensionless.


m_(\parallel) - Slope, dimensionless.

Its slope is the slope of the given, which must be transformed into its explicitive form:


-8\cdot x + 5\cdot y = 89


5\cdot y = 89 +8\cdot x


y = (89)/(5)+(8)/(5) \cdot x

The slope of the parallel line is
(8)/(5).

If
x_(o) = -8,
y_(o) = 1 and
m_(\parallel) = (8)/(5), then:


y-1 = (8)/(5)\cdot [x-(-8)]


y-1 = (8)/(5)\cdot x +(64)/(5)


y = (8)/(5)\cdot x +(69)/(5)

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:


y-y_(o) = m_(\perp)\cdot (x-x_(o))

Where:


x_(o),
y_(o) - Components of the given point, dimensionless.


m_(\perp) - Slope, dimensionless.

Besides, a slope that is perpendicular to original line can be calculated by this expression:


m_(\perp) = -(1)/(m)

Where
m is the slope of the original line, dimensionless.

The original slope is determined from the explicitive form of the given line:


-5\cdot x +9\cdot y = 49


9\cdot y = 49+5\cdot x


y = (49)/(9) +(5)/(9)\cdot x

The original slope is
(5)/(9), and the slope of the perpendicular line is:


m_(\perp) = -(1)/(m)


m_(\perp) = -(1)/((5)/(9) )


m_(\perp) = -(9)/(5)

If
x_(o) = -8,
y_(o) = 1 and
m_(\perp) = -(9)/(5), then:


y-1 = -(9)/(5)\cdot [x-(-8)]


y-1 = -(9)/(5)\cdot x-(72)/(5)


y = -(9)/(5)\cdot x -(67)/(5)

The correct answer is A.

User OrS
by
5.1k points
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