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Vikki [24]
3 years ago
11

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

Mathematics
1 answer:
barxatty [35]3 years ago
4 0

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

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