Answer : x=3
we need to find the input value produces the same output value for the two fictions on the graph
To find input value x that gives the same output y , we look at the intersection of both graphs
Both lines on graph intersects at (3,-1)
When input x=3 then output y=-1
Now we verify with given equations
Plug in 3 for x in f(x)
[tex]f(x)= \frac{-2}{3}x+ 1[/tex]
[tex]f(3)= \frac{-2}{3}(3) + 1=-1[/tex]
Plug in 3 for x in g(x)
[tex]g(x)= \frac{1}{3}x-2[/tex]
[tex]g(3)= \frac{1}{3}(3)-2=-1[/tex]
So when input x=3 the output is y=-1
x=3 is the final answer
