Question

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

Explanation:

Step1: Set \( f(x) = g(x) \)

To find the \( x \)-value where the two functions intersect, we set \( -\frac{2}{3}x + 1=\frac{1}{3}x - 2 \).

Step2: Combine like terms

Add \( \frac{2}{3}x \) to both sides: \( 1=\frac{1}{3}x+\frac{2}{3}x - 2 \), which simplifies to \( 1 = x - 2 \).

Step3: Solve for \( x \)

Add 2 to both sides: \( x=1 + 2=3 \).
Alternatively, from the graph, the intersection point has an \( x \)-coordinate of 3.

Answer:

\( x = 3 \) (corresponding to the option: \( x = 3 \))