1. The problem is to graph the equation $y = x + 4$. 2. This is a linear equation with a slope of 1 and a y-intercept at $(0, 4)$, meaning the line crosses the y-axis at 4. 3. To sketch the graph, plot the intercept point $(0, 4)$. 4. Use the slope to find another point: since slope is 1, for each increase of 1 in $x$, $y$ increases by 1. For example, when $x = 1$, $y = 5$; when $x = -1$, $y = 3$. 5. Connect these points to form a diagonal line rising to the right. 6. The graph shown with a horizontal line at $y = 5$ and points $(-6, 5)$ and $(6, 5)$ does not represent $y = x + 4$. A horizontal line has a slope $0$, which contradicts the slope 1 of $y = x + 4$. 7. Therefore, the correct graph of $y = x + 4$ is a diagonal line crossing the y-axis at 4 and increasing one unit up for each unit right on the x-axis.