Graph the line using the slope and $$ \dot{y} $$-intercept. Graph the line through the point $$ (0,3) $$, having a slope of -3 .

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To graph the line passing through the point $$(0, 3)$$ with a slope of $$-3$$, follow these steps:

### 1. **Understand the Components**

- **Slope ($$m$$)**: The slope of the line is $$-3$$. This means that for every 1 unit you move to the right (positive direction on the x-axis), the line moves down 3 units (negative direction on the y-axis).
  
- **Y-intercept ($$b$$)**: The y-intercept is the point where the line crosses the y-axis. Here, it is given as $$(0, 3)$$.

### 2. **Write the Equation of the Line**

Using the slope-intercept form of a line:
$$
y = mx + b
$$
Substitute the given slope and y-intercept:
$$
y = -3x + 3
$$

### 3. **Plot the Y-intercept**

- Start by plotting the y-intercept $$(0, 3)$$ on the graph.

### 4. **Use the Slope to Find Another Point**

- The slope $$-3$$ can be expressed as a fraction $$-\frac{3}{1}$$, which means:
  - **Rise (vertical change)**: $$-3$$ (move down 3 units)
  - **Run (horizontal change)**: $$1$$ (move right 1 unit)

- Starting from $$(0, 3)$$, move right 1 unit to $$x = 1$$ and down 3 units to $$y = 0$$. This gives the point $$(1, 0)$$.

### 5. **Plot the Second Point**

- Plot the point $$(1, 0)$$ on the graph.

### 6. **Draw the Line**

- Draw a straight line passing through the two plotted points $$(0, 3)$$ and $$(1, 0)$$.
- Extend the line in both directions, adding arrows to indicate that it continues indefinitely.

### 7. **Graphical Representation**

Since I can't provide a visual graph here, here's a simple representation using text:

```
y
|
4 |         
3 | • (0,3)
2 |          
1 |          
0 |----------• (1,0)-------- x
```

- The dot at $$(0, 3)$$ is the y-intercept.
- The dot at $$(1, 0)$$ is the second point derived from the slope.
- The line passes through these points and extends beyond them in both directions.

### 8. **Verification**

To ensure the accuracy of the graph, you can plug in additional values of $$x$$ into the equation $$y = -3x + 3$$ to find corresponding $$y$$ values and plot more points if needed. For example:

- When $$x = 2$$:
  $$
  y = -3(2) + 3 = -6 + 3 = -3 \quad \Rightarrow \quad (2, -3)
  $$

- When $$x = -1$$:
  $$
  y = -3(-1) + 3 = 3 + 3 = 6 \quad \Rightarrow \quad (-1, 6)
  $$

Plotting these additional points will help confirm that the line is correctly graphed.

### 9. **Final Graph**

The final graph will show a straight line descending from left to right, crossing the y-axis at $$(0, 3)$$ with a slope of $$-3$$.

---

**Summary:**
- **Equation**: $$ y = -3x + 3 $$
- **Slope**: $$-3$$ (down 3 units for every 1 unit right)
- **Y-intercept**: $$(0, 3)$$
- **Another Point**: $$(1, 0)$$

Plot these points and draw a straight line through them to graph the desired line.
To graph the line with a slope of -3 passing through the point (0, 3), plot the y-intercept at (0, 3). Then, move right 1 unit and down 3 units to find another point at (1, 0). Draw a straight line through these points to complete the graph.

Graph the line using the slope and -intercept.
Graph the line through the point , having a slope of -3 .

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Graph the line using the slope and -intercept. Graph the line through the point , having a slope of -3 .