1. The problem is to graph the function $g(x) = \frac{1}{4}x$. 2. This is a linear function of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. For $g(x) = \frac{1}{4}x$, the slope $m = \frac{1}{4}$ and the y-intercept $b = 0$. 4. The slope $\frac{1}{4}$ means that for every 4 units you move horizontally to the right, the function value increases by 1 unit. 5. To graph, start at the origin $(0,0)$ since $b=0$. 6. From $(0,0)$, move 4 units to the right to $(4,0)$ and then 1 unit up to $(4,1)$. 7. Plot these points and draw a straight line through them extending in both directions. 8. The graph passes through the origin and rises slowly because the slope is less than 1. Final answer: The graph of $g(x) = \frac{1}{4}x$ is a straight line through the origin with slope $\frac{1}{4}$.