Answer:
B.
[tex]x=\frac{9}{x}[/tex]
Step-by-step explanation:
Firstly, we will identify type of functions
and then we can set them equal
Blue curve:
We can see that
this is curve is inversly proportional type curve
so, we write function as
[tex]y=\frac{k}{x}[/tex]
we can select anyone point and find k
we can see that intersection point is (3,3)
so, we can plug x=3 and y=3 and find k
[tex]3=\frac{k}{3}[/tex]
[tex]k=9[/tex]
now, we can plug it back
[tex]y=\frac{9}{x}[/tex]
Red curve:
we can see that this is the line
so, we can select any two points and find equation of that line
First point is (0,0)
so, x1=0 , y1=0
Second point is (3,3)
so, x2=3 , y2=3
Firstly, we can find slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{3-0}{3-0}[/tex]
[tex]m=1[/tex]
now, we can use point slope form of line
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-0=1(x-0)[/tex]
[tex]y=x[/tex]
since, we have got two equations
and we have to find intersection points
so, we can set them equal
[tex]y=\frac{9}{x}=x[/tex]
[tex]\frac{9}{x}=x[/tex]
So, answer is
[tex]x=\frac{9}{x}[/tex]
