To identify the correct graph of $y = 3x + 4$, let's analyze the equation and check the graphs:

1. Equation Analysis:

   • The equation $y = 3x + 4$ is in slope-intercept form $y = mx + b$.
   • Here, $m = 3$, which means the slope is 3, indicating a line that rises quickly.
   • The $y$-intercept $b = 4$ means the line crosses the $y$-axis at 4.

2. Identifying Key Features:

   • The line should intersect the $y$-axis at $y = 4$.
   • With a slope of 3, the line should rise 3 units for every 1 unit it moves to the right.

3. Checking the Graphs:

   • By looking at each option, focus on which line has a positive slope and crosses the $y$-axis at $y = 4$.

Please let me know if you'd like a step-by-step breakdown of how each graph fits or doesn’t fit these criteria, and I can help pinpoint the correct one based on that.

Here are five related questions for deeper understanding:

1. How does the slope affect the angle of the line?
2. What would happen to the graph if we changed the equation to $y = -3x + 4$?
3. How do we find the $x$-intercept from the equation?
4. What does it mean if a line is parallel or perpendicular to another line?
5. How would the graph change if we moved the line up or down on the $y$-axis?

Tip: For graphing linear equations, always identify the slope and the intercept first to sketch it quickly.