1. The problem is to graph the linear equation $y = 3x + 4$. 2. This equation is in slope-intercept form, where the slope $m = 3$ and the y-intercept $b = 4$. 3. The y-intercept means the graph crosses the y-axis at the point $(0,4)$. 4. The slope $3$ means for every increase of 1 in $x$, $y$ increases by 3. 5. To plot the graph, start at point $(0,4)$, then move 1 unit right and 3 units up to reach point $(1,7)$. 6. Connecting these points with a straight line produces the graph of $y = 3x + 4$. Final answer: the line has slope 3 and y-intercept 4, plotted as described.