Question

Helppppppp. Find k if the lines 3x-5y=9 & 2x+ky=11 are a)parallel and b)perpendicular

Answer 1

For lines to be parallel, they have to have the same slopes. For the equation given as Ax + By + C = 0, the slope is -A / B. Equating the slopes of the given equations of lines,
- (3 / -5) = - (2 / k)
The value of k is equal to -10/3.

Answer 2

a)
`k=-(10)/(3)`

b)
`k=(6)/(5)`

Explanation:

If two lines
`y = m_1x+c_1` and
`y=m_2x+c_2` ( where,
`m_1` and
`m_2` are their slope respectively ) are,

Parallel, if,

`m_1=m_2`

Perpendicular, if,

`m_1* m_2 = -1`

Here, the lines are,

3x - 5y = 9 ⇒ 5y = 3x - 9 ⇒
`y=(3)/(5)x-(9)/(5)`

2x + ky = 11 ⇒ ky = -2x + 11 ⇒
`y=-(2)/(k)x + 11`

a) If they are parallel,

`(3)/(5)=-(2)/(k)\implies 3k=-10\implies k=-(10)/(3)`

b) If they are perpendicular,

`(3)/(5)* -(2)/(k)=-1\implies -(6)/(5k)=-1\implies k=(6)/(5)`