1. The problem is to understand how changing the value of $b$ in the linear equation $y = x + b$ affects the graph of the line. 2. The equation $y = x + b$ represents a straight line with slope $1$ and $y$-intercept $b$. 3. The slope $1$ means the line rises one unit vertically for every one unit it moves horizontally. 4. The $y$-intercept $b$ is the point where the line crosses the $y$-axis. 5. When $b = 0$, the line passes through the origin $(0,0)$. 6. Increasing $b$ shifts the entire line upward by $b$ units without changing its slope. 7. Decreasing $b$ shifts the line downward by $|b|$ units, again without changing the slope. 8. The slope remains constant at $1$, so the steepness of the line does not change when $b$ changes. 9. Therefore, the correct statement is: "If the value of $b$ is increased from $0$, the graph moves up."