Graph the line with the given point and slope. The line through $$ (-1,0) $$ with slope $$ \frac{5}{2} $$.

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To graph the line that passes through the point $$(-1, 0)$$ with a slope of $$\frac{5}{2}$$, follow these steps:

### 1. Understand the Slope

The slope ($$m$$) of $$\frac{5}{2}$$ means that for every **2 units** you move **horizontally** (along the x-axis), the line rises **5 units** vertically (along the y-axis).

### 2. Use the Point-Slope Form to Find the Equation of the Line

The **point-slope form** of a line's equation is:

$$
y - y_1 = m(x - x_1)
$$

Where:
- $$m$$ is the slope
- $$(x_1, y_1)$$ is a point on the line

Plugging in the given point $$(-1, 0)$$ and slope $$\frac{5}{2}$$:

$$
y - 0 = \frac{5}{2}(x - (-1))
$$
$$
y = \frac{5}{2}(x + 1)
$$
$$
y = \frac{5}{2}x + \frac{5}{2}
$$

So, the **slope-intercept form** of the equation is:

$$
y = \frac{5}{2}x + \frac{5}{2}
$$

### 3. Plot the Given Point

Start by plotting the point $$(-1, 0)$$ on the coordinate plane.

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

From $$(-1, 0)$$:
- **Rise**: $$5$$ units (since the slope is $$\frac{5}{2}$$)
- **Run**: $$2$$ units

This means if you move **2 units to the right** (from $$x = -1$$ to $$x = 1$$), you move **5 units up** (from $$y = 0$$ to $$y = 5$$).

So, another point on the line is $$(1, 5)$$.

### 5. Draw the Line

Connect the two points $$(-1, 0)$$ and $$(1, 5)$$ with a straight line. Extend the line in both directions.

### 6. Additional Points (Optional)

To ensure accuracy, you can plot additional points:

- For $$x = 3$$:
  $$
  y = \frac{5}{2}(3) + \frac{5}{2} = \frac{15}{2} + \frac{5}{2} = \frac{20}{2} = 10
  $$
  So, the point is $$(3, 10)$$.

- For $$x = -3$$:
  $$
  y = \frac{5}{2}(-3) + \frac{5}{2} = -\frac{15}{2} + \frac{5}{2} = -\frac{10}{2} = -5
  $$
  So, the point is $$(-3, -5)$$.

### 7. Graphical Representation

While I can't provide an actual image, here's a rough sketch of how the graph would look:

```
y
|
10 |                 *
 9 |
 8 |
 7 |
 6 |             *
 5 |         *
 4 |
 3 |
 2 |
 1 |
 0 |     *
-1 |
-2 |
-3 | 
   --------------------------- x
     -4 -3 -2 -1 0 1 2 3 4
```

- The asterisks (*) represent points on the line:
  - $$(-1, 0)$$
  - $$(1, 5)$$
  - $$(3, 10)$$

### 8. Summary

- **Equation of the Line**: $$y = \frac{5}{2}x + \frac{5}{2}$$
- **Slope**: $$\frac{5}{2}$$ (rise over run)
- **Key Points**: $$(-1, 0)$$, $$(1, 5)$$, $$(3, 10)$$, $$(-3, -5)$$

By plotting these points and drawing a straight line through them, you'll have the graph of the desired line.
To graph the line passing through $$(-1, 0)$$ with a slope of $$\frac{5}{2}$$, plot the point $$(-1, 0)$$ and another point using the slope (e.g., $$(1, 5)$$), then draw a straight line through them.

Graph the line with the given point and slope. The line through \( (-1,0) \) with slope \( \frac{5}{2} \).

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