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))](https://img.qammunity.org/2021/formulas/mathematics/high-school/fynre62mscprxzjc7lwouiylh9jztsatkb.png)
Where:
,
- Components of the given point, dimensionless.
- Slope, dimensionless.
Besides, a slope that is perpendicular to original line can be calculated by this expression:
![m_(\perp) = -(1)/(m)](https://img.qammunity.org/2021/formulas/sat/college/hqhhfi7f7h9d1ehvk1bxnrtxddo84tq0ws.png)
Where
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](https://img.qammunity.org/2021/formulas/mathematics/high-school/qik6bm4let1r9yt0fx7fan6d1duy122xfv.png)
![2\cdot x +5\cdot y = 19](https://img.qammunity.org/2021/formulas/mathematics/high-school/60fuzi2ewu0k8r3efwhmeamh5clfzqi7mj.png)
![5\cdot y = 19 - 2\cdot x](https://img.qammunity.org/2021/formulas/mathematics/high-school/95y0fc85rb8dzk85ufpxx3jg6zrlcu0u0o.png)
![y = (19)/(5) -(2)/(5)\cdot x](https://img.qammunity.org/2021/formulas/mathematics/high-school/chx97s7bi0fhi3odxez7qgqmayl90t1fza.png)
The original slope is
, and the slope of the perpendicular line is:
![m_(\perp) = -(1)/(\left(-(2)/(5)\right) )](https://img.qammunity.org/2021/formulas/mathematics/high-school/ktq8ovv2raic20vfg05sbf6cqh1g5dv4u0.png)
![m_(\perp) = (5)/(2)](https://img.qammunity.org/2021/formulas/mathematics/high-school/w9yccojmsg8t0ylx56quskdl54xu2kj88r.png)
If
,
and
, then:
![y-(-5) = (5)/(2)\cdot [x-(-3)]](https://img.qammunity.org/2021/formulas/mathematics/high-school/i1hkz0plv06y12ude4o5n1b0d6hg0nee3z.png)
![y + 5 = (5)/(2)\cdot x +(15)/(2)](https://img.qammunity.org/2021/formulas/mathematics/high-school/gu4wjjkljfnc4a1sbff5a8e8lg0t1tyd77.png)
![y = (5)/(2)\cdot x +(5)/(2)](https://img.qammunity.org/2021/formulas/mathematics/high-school/cxya6cn4kfkx6d7wov9qx0hrshibwipfoy.png)
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))](https://img.qammunity.org/2021/formulas/mathematics/high-school/982fj9d919ur0hkucnhkxfe0c2ogi6x232.png)
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:
![-8\cdot x + 5\cdot y = 89](https://img.qammunity.org/2021/formulas/mathematics/high-school/vqbi8ffwf4p0nx8ajmz9biv0pucxdizfba.png)
![5\cdot y = 89 +8\cdot x](https://img.qammunity.org/2021/formulas/mathematics/high-school/ugp7r8fqxb1k40fng5i3dxrtl5eulepgzj.png)
![y = (89)/(5)+(8)/(5) \cdot x](https://img.qammunity.org/2021/formulas/mathematics/high-school/bw9lbmhn0ej2dtqr16gea1zx6h9z8znmqm.png)
The slope of the parallel line is
.
If
,
and
, then:
![y-1 = (8)/(5)\cdot [x-(-8)]](https://img.qammunity.org/2021/formulas/mathematics/high-school/qlxnlp7mprm46th8zzy47radqz0v0gbh6n.png)
![y-1 = (8)/(5)\cdot x +(64)/(5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/v9p05g39gu28dzr9l01zbbn1hx023bbjlj.png)
![y = (8)/(5)\cdot x +(69)/(5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/a13q9hcx0equvny3buxgnqeba0n8089a5r.png)
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))](https://img.qammunity.org/2021/formulas/mathematics/high-school/fynre62mscprxzjc7lwouiylh9jztsatkb.png)
Where:
,
- Components of the given point, dimensionless.
- Slope, dimensionless.
Besides, a slope that is perpendicular to original line can be calculated by this expression:
![m_(\perp) = -(1)/(m)](https://img.qammunity.org/2021/formulas/sat/college/hqhhfi7f7h9d1ehvk1bxnrtxddo84tq0ws.png)
Where
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](https://img.qammunity.org/2021/formulas/mathematics/high-school/l2cvh0tnehuhkefnsqzt2j4q8m1lj5w0ur.png)
![9\cdot y = 49+5\cdot x](https://img.qammunity.org/2021/formulas/mathematics/high-school/iw3r6phy00riwhhwklijtnu2ayswl422b6.png)
![y = (49)/(9) +(5)/(9)\cdot x](https://img.qammunity.org/2021/formulas/mathematics/high-school/ju3ycal3zcum1wxwmtejeuy6bfttdo4ebc.png)
The original slope is
, and the slope of the perpendicular line is:
![m_(\perp) = -(1)/(m)](https://img.qammunity.org/2021/formulas/sat/college/hqhhfi7f7h9d1ehvk1bxnrtxddo84tq0ws.png)
![m_(\perp) = -(1)/((5)/(9) )](https://img.qammunity.org/2021/formulas/mathematics/high-school/z0xithkuikf6znlivv310ik6dvxdlpdz2u.png)
![m_(\perp) = -(9)/(5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/g2u908h2a6493dulde7mntsa3f4o6kqb8k.png)
If
,
and
, then:
![y-1 = -(9)/(5)\cdot [x-(-8)]](https://img.qammunity.org/2021/formulas/mathematics/high-school/1vvohbraepny56uhnsmr4rio99hgq2xqav.png)
![y-1 = -(9)/(5)\cdot x-(72)/(5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/m53o85xh2kfq63mqu2422cn1ipvdo3duf4.png)
![y = -(9)/(5)\cdot x -(67)/(5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/za642k75t01c67a0pw737sn3zp8ldye3y4.png)
The correct answer is A.