which input value produces the same output value for the two functions on the graph?\n$f(x)=-\frac{2}{3}x +…

Answer:

$x = 3$

Explanation:

Step1: Set the two functions equal.

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

Step2: Add $\frac{2}{3}x$ to both sides.

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

Step3: Combine like - terms.

$1 = x-2$

Step4: Add 2 to both sides.

$x=3$ We can also observe from the graph that the two lines $y = f(x)$ and $y = g(x)$ intersect at the point $(3,-1)$. At the intersection point, the $x$ - value (input) gives the same $y$ - value (output) for both functions.