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

$y=-\frac{4}{a} x+\frac{8}{a}$

we can find slope

so, we get

$m_1=-\frac{4}{a}$

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

$y=\frac{9}{a} +\frac{5}{a}$

we can find slope

$m_2=\frac{9}{a}$

we are given both lines are perpendicular

so, the multiplication of their slopes must  be -1

$m_1\times m_2=-1$

we can plug values

$-\frac{4}{a}\times \frac{9}{a}=-1$

now, we can solve for a

$\frac{36}{a^2}=-1$

Multiply both sides by a

$\frac{36}{a^2}\times a^2=1\times a^2$

$36= a^2$

now, we can solve for a

we get

$a=-6,a=6$...............Answer