Plot the intercepts to graph the equation. 

3x-2y=-6




To plot the intercepts and graph the equation \(3x - 2y = -6\), we need to find the x-intercept and y-intercept.

### Finding the Intercepts

#### X-intercept
The x-intercept occurs when \(y = 0\).

\[
3x - 2(0) = -6 \implies 3x = -6 \implies x = -2
\]

So, the x-intercept is \((-2, 0)\).

#### Y-intercept
The y-intercept occurs when \(x = 0\).

\[
3(0) - 2y = -6 \implies -2y = -6 \implies y = 3
\]

So, the y-intercept is \((0, 3)\).

### Graphing the Equation

1. Plot the x-intercept \((-2, 0)\).
2. Plot the y-intercept \((0, 3)\).
3. Draw a straight line through these two points.

Here's the graph of the equation:

\[
\begin{array}{c|c|c}
x & y & \text{Points} \\
\hline
-2 & 0 & (-2, 0) \\
0 & 3 & (0, 3) \\
\end{array}
\]

Now, let's plot this.

```python
import matplotlib.pyplot as plt
import numpy as np

# Define the function to plot the line
def plot_line():
    x = np.linspace(-4, 4, 400)
    y = (3/2)*x + 3
    
    plt.figure(figsize=(8, 6))
    plt.plot(x, y, '-r', label='3x - 2y = -6')
    plt.plot(-2, 0, 'bo')  # x-intercept
    plt.plot(0, 3, 'bo')   # y-intercept
    plt.axhline(0, color='black',linewidth=0.5)
    plt.axvline(0, color='black',linewidth=0.5)
    plt.grid(color = 'gray', linestyle = '--', linewidth = 0.5)
    plt.legend(loc='best')
    plt.title('Graph of 3x - 2y = -6')
    plt.xlabel('x')
    plt.ylabel('y')
    plt.xlim(-4, 4)
    plt.ylim(-4, 4)
    plt.show()

plot_line()
```

The graph shows the line passing through the intercepts \((-2, 0)\) and \((0, 3)\).

Would you like more details or have any questions?

Here are 5 more questions you might want to explore:
1. How do you find the slope of a line given an equation?
2. How do you convert a standard form equation to slope-intercept form?
3. How do you find the equation of a line given two points?
4. What are parallel and perpendicular lines in terms of slopes?
5. How can you determine if a point lies on a given line?

**Tip:** When graphing linear equations, always start by finding the intercepts to make the graphing process easier.

Learn how to graph the linear equation 3x - 2y = -6 by finding its intercepts and plotting them. This problem covers key algebraic concepts, including linear equations and graphing techniques. Suitable for students in Grades 7-9.

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