3.) Graph the equation on the coordinate grid. $$ y=\frac{1}{3} x+2 $$

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To graph the linear equation $$ y = \frac{1}{3}x + 2 $$ on a coordinate grid, follow these steps:

### 1. Understand the Equation Format
The equation is in the slope-intercept form:
$$ y = mx + b $$
where:
- **$$ m $$** is the **slope** of the line.
- **$$ b $$** is the **y-intercept**, the point where the line crosses the y-axis.

For your equation:
- **Slope ($$ m $$) =** $$ \frac{1}{3} $$
- **Y-intercept ($$ b $$) =** 2

### 2. Plot the Y-Intercept
Start by plotting the y-intercept on the graph.
- Locate the y-axis (vertical axis).
- Find the point (0, 2) because when $$ x = 0 $$, $$ y = 2 $$.
  
**Point A:** (0, 2)

### 3. Use the Slope to Find Another Point
The slope $$ \frac{1}{3} $$ means that for every **rise** of 1 unit, there is a **run** of 3 units.

- **From Point A (0, 2):**
  - **Rise:** Move **up** 1 unit.
  - **Run:** Move **right** 3 units.
  
- This brings you to the point (3, 3).

**Point B:** (3, 3)

### 4. Plot the Second Point
Plot the second point you just found.

### 5. Draw the Line
Use a ruler to draw a straight line passing through both points A and B. Extend the line in both directions.

### 6. (Optional) Find the X-Intercept
To find where the line crosses the x-axis ($$ y = 0 $$), set $$ y $$ to 0 and solve for $$ x $$:

$$
0 = \frac{1}{3}x + 2 \
\frac{1}{3}x = -2 \
x = -6
$$

So, the x-intercept is at (-6, 0).

**Point C:** (-6, 0)

You can plot this third point to ensure your line is accurate.

### 7. Final Graph

Here's a rough sketch of how the graph should look:

```
y
|
6|
5|
4|
3|        B (3,3)
2| A (0,2)
1|
0|---------C(-6,0)-------- x
```

- **Point A (0, 2):** Y-intercept.
- **Point B (3, 3):** Using the slope.
- **Point C (-6, 0):** X-intercept.

### Summary

- **Slope ( $$ m = \frac{1}{3} $$ ):** For every 3 units you move to the right on the x-axis, move up 1 unit on the y-axis.
- **Y-Intercept ( $$ b = 2 $$ ):** The line crosses the y-axis at (0, 2).
- **Drawing the Line:** Connect the points A and B (and optionally C) with a straight line extending in both directions.

By following these steps, you should have an accurate graph of the equation $$ y = \frac{1}{3}x + 2 $$.
To graph the equation $$ y = \frac{1}{3}x + 2 $$: 1. **Plot the Y-Intercept:** Start at (0, 2). 2. **Use the Slope:** Move up 1 unit and right 3 units to reach (3, 3). 3. **Draw the Line:** Connect (0, 2) and (3, 3) with a straight line. Optionally, find the X-Intercept at (-6, 0) by setting $$ y = 0 $$ and solving for $$ x $$.

3.) Graph the equation on the coordinate grid. \[ y=\frac{1}{3} x+2 \]

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