Question

which input value produces the same output value for the two functions on the graph?

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

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

Explanation:

Identify the graphical intersection

Using the Graphical Intersection knowledge point

$$ \text{Intersection point on the graph: } (3, -1) $$

Set up the algebraic system

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK0
$$

Solve for the input value

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK1
$$

Verify the output value

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK2
$$

Answer:

\(x = 3\)