The problem asks us to sketch the graph of the line given by the equation $y = \frac{1}{4}x - 3$.

1. Problem Description

The problem asks us to sketch the graph of the line given by the equation $y = \frac{1}{4}x - 3$.

2. Solution Steps

The given equation is in the slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

In our case, $m = \frac{1}{4}$ and $b = -3$. This means that the line intersects the y-axis at the point $(0, -3)$.

To find another point on the line, we can choose a value for $x$ and calculate the corresponding $y$ value.

Let's choose $x = 4$. Then $y = \frac{1}{4}(4) - 3 = 1 - 3 = -2$. So, another point on the line is $(4, -2)$.

Now we have two points: $(0, -3)$ and $(4, -2)$.

We can plot these points on the coordinate plane and draw a line through them to sketch the graph of the equation.

3. Final Answer

The graph is a line passing through the points $(0, -3)$ and $(4, -2)$. (Note: I cannot actually sketch the graph here, but this description allows you to do so.)