Question

Jika garis 4x+ay = 8 dan ay=9x + 5 saling tegak lurus,maka nilai a

Answer 1

We are given equations as

`4x+ay=8`

Firstly, we will write in slope intercept form of line

y=mx+b

`4x+ay=8`

Subtract both sides by 4x

`4x+ay-4x=-4x+8`

`ay=-4x+8`

now, we can divide both sides by a

`y=-(4)/(a) x+(8)/(a)`

we can find slope

so, we get

`m_1=-(4)/(a)`

we are given second equation as

`ay=9x+5`

Firstly, we will write in slope intercept form of line

y=mx+b

divide both sides by a

`y=(9)/(a) +(5)/(a)`

we can find slope

`m_2=(9)/(a)`

we are given both lines are perpendicular

so, the multiplication of their slopes must be -1

`m_1* m_2=-1`

we can plug values

`-(4)/(a)* (9)/(a)=-1`

now, we can solve for a

`(36)/(a^2)=-1`

Multiply both sides by a

`(36)/(a^2)* a^2=1* a^2`

`36= a^2`

now, we can solve for a

we get

`a=-6,a=6`...............Answer