1. The problem is to solve the equation $4x + 1 = -x + 6$ graphically. 2. To do this, we graph the functions $f(x) = 4x + 1$ and $g(x) = -x + 6$ on the same set of axes. 3. The solution to the equation is the $x$-value(s) where the graphs of $f$ and $g$ intersect. 4. Set the two functions equal to find the intersection algebraically: $$4x + 1 = -x + 6$$ 5. Add $x$ to both sides: $$4x + x + 1 = 6$$ $$5x + 1 = 6$$ 6. Subtract 1 from both sides: $$5x = 5$$ 7. Divide both sides by 5: $$x = 1$$ 8. So, the graphs intersect at $x = 1$, which is the solution to the equation. 9. To verify, plug $x=1$ into both functions: $$f(1) = 4(1) + 1 = 5$$ $$g(1) = -1 + 6 = 5$$ Both equal 5, confirming the intersection point is $(1,5)$. Final answer: The solution is $x = 1$.