1. **State the problem:** We are given the linear equation $5x - 3y = 4$ and the function $f(x) = \frac{5}{3}x - \frac{4}{3}$. We want to verify if $f(2) = 2$ is correct. 2. **Rewrite the equation in function form:** Solve for $y$ in terms of $x$ from the equation $5x - 3y = 4$. 3. **Isolate $y$:** $$5x - 3y = 4$$ $$-3y = 4 - 5x$$ $$y = \frac{4 - 5x}{-3} = \frac{-4 + 5x}{3} = \frac{5}{3}x - \frac{4}{3}$$ 4. **Compare with given function:** The function $f(x) = \frac{5}{3}x - \frac{4}{3}$ matches the expression for $y$. 5. **Evaluate $f(2)$:** $$f(2) = \frac{5}{3} \times 2 - \frac{4}{3} = \frac{10}{3} - \frac{4}{3} = \frac{6}{3} = 2$$ 6. **Conclusion:** The evaluation $f(2) = 2$ is correct and consistent with the original equation. This confirms that the function $f(x)$ correctly represents the line given by $5x - 3y = 4$ and the value at $x=2$ is indeed 2.