Question

What input value produces the same output value for the two fictions on the graph?

Answer 1

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)  

$f(x)= \frac{-2}{3}x+ 1$

$f(3)= \frac{-2}{3}(3) + 1=-1$

Plug in 3 for x in   g(x)

$g(x)= \frac{1}{3}x-2$

$g(3)= \frac{1}{3}(3)-2=-1$

So when input x=3  the output is y=-1

x=3 is the final answer