Question

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

Answer 1

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.