Graph the line. $$ y=\frac{1}{4} x+4 $$

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To graph the line given by the equation

$$
y = \frac{1}{4} x + 4,
$$

we can follow these steps:

1. **Identify the slope and y-intercept**:
   - The slope $$ m $$ is $$ \frac{1}{4} $$.
   - The y-intercept $$ b $$ is $$ 4 $$. This means the line crosses the y-axis at the point $$ (0, 4) $$.

2. **Plot the y-intercept**:
   - Start by plotting the point $$ (0, 4) $$ on the graph.

3. **Use the slope to find another point**:
   - The slope $$ \frac{1}{4} $$ means that for every 4 units you move up in the y-direction, you move 1 unit to the right in the x-direction.
   - From the point $$ (0, 4) $$, move 1 unit to the right (to $$ x = 1 $$) and 4 units up (to $$ y = 8 $$). This gives us the point $$ (1, 8) $$.

4. **Draw the line**:
   - Connect the points $$ (0, 4) $$ and $$ (1, 8) $$ with a straight line. Extend the line in both directions.

5. **Check additional points**:
   - You can also find more points by substituting different values for $$ x $$ into the equation. For example:
     - If $$ x = -4 $$:
       $$
       y = \frac{1}{4}(-4) + 4 = -1 + 4 = 3 \quad \text{(point: } (-4, 3) \text{)}
       $$
     - If $$ x = 4 $$:
       $$
       y = \frac{1}{4}(4) + 4 = 1 + 4 = 5 \quad \text{(point: } (4, 5) \text{)}
       $$

By plotting these points and drawing the line through them, you will have the graph of the line $$ y = \frac{1}{4} x + 4 $$.
To graph the line $$ y = \frac{1}{4} x + 4 $$, plot the y-intercept at $$ (0, 4) $$, use the slope $$ \frac{1}{4} $$ to find another point like $$ (1, 8) $$, and draw a straight line through these points.

Graph the line. \[ y=\frac{1}{4} x+4 \]

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