We are given equations as
[tex]4x+ay=8[/tex]
Firstly, we will write in slope intercept form of line
y=mx+b
[tex]4x+ay=8[/tex]
Subtract both sides by 4x
[tex]4x+ay-4x=-4x+8[/tex]
[tex]ay=-4x+8[/tex]
now, we can divide both sides by a
[tex]y=-\frac{4}{a} x+\frac{8}{a}[/tex]
we can find slope
so, we get
[tex]m_1=-\frac{4}{a}[/tex]
we are given second equation as
[tex]ay=9x+5[/tex]
Firstly, we will write in slope intercept form of line
y=mx+b
divide both sides by a
[tex]y=\frac{9}{a} +\frac{5}{a}[/tex]
we can find slope
[tex]m_2=\frac{9}{a}[/tex]
we are given both lines are perpendicular
so, the multiplication of their slopes must be -1
[tex]m_1\times m_2=-1[/tex]
we can plug values
[tex]-\frac{4}{a}\times \frac{9}{a}=-1[/tex]
now, we can solve for a
[tex]\frac{36}{a^2}=-1[/tex]
Multiply both sides by a
[tex]\frac{36}{a^2}\times a^2=1\times a^2[/tex]
[tex]36= a^2[/tex]
now, we can solve for a
we get
[tex]a=-6,a=6[/tex]...............Answer
