The function $f(x) = \frac{5}{4}x + 2$ is a linear equation representing a straight line. Here's how it is graphed:

Key Characteristics:

1. Slope (m): $\frac{5}{4}$
   This means the line rises by 5 units for every 4 units it moves to the right.

2. Y-intercept (b): $2$
   This is the point where the line crosses the y-axis, at $(0, 2)$.

Steps to Graph:

1. Plot the y-intercept: Start at $(0, 2)$ on the graph.
2. Use the slope: From $(0, 2)$, move up 5 units and right 4 units to get another point, $(4, 7)$. Similarly, move down 5 units and left 4 units to get $(-4, -3)$.
3. Draw the line: Connect these points with a straight line extending in both directions.

Would you like me to generate the actual graph of this function? Let me know!