1. The problem asks to solve the equation $5x + 1 = -x + 7$ graphically by plotting two functions and finding their intersection points. 2. We define the functions: - $f(x) = 5x + 1$ - $g(x) = -x + 7$ 3. To solve graphically, plot both $f(x)$ and $g(x)$ on the same coordinate plane. 4. The solution to the equation corresponds to the $x$-values where the graphs of $f$ and $g$ intersect. 5. To find the intersection algebraically (to verify), set $f(x) = g(x)$: $$5x + 1 = -x + 7$$ 6. Solve for $x$: $$5x + x = 7 - 1$$ $$6x = 6$$ $$x = 1$$ 7. Substitute $x=1$ into either function to find $y$: $$f(1) = 5(1) + 1 = 6$$ 8. Therefore, the graphs intersect at the point $(1, 6)$, which is the solution to the equation. Final answer: $x = 1$