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Let's analyze the given system of linear equations:

1. **Equation 1**: \( 8x - 4y = 12 \)
2. **Equation 2**: \( -6x + 3y = -9 \)

To determine the relationship between the graphs of these two lines, we should first rewrite each equation in slope-intercept form (\( y = mx + b \)), where \( m \) is the slope.

### Step 1: Finding the slope of the first equation
Starting with \( 8x - 4y = 12 \):
\[
-4y = -8x + 12
\]
\[
y = 2x - 3
\]
So, the slope of the first line is \( m_1 = 2 \).

### Step 2: Finding the slope of the second equation
Starting with \( -6x + 3y = -9 \):
\[
3y = 6x - 9
\]
\[
y = 2x - 3
\]
So, the slope of the second line is \( m_2 = 2 \).

### Step 3: Analyzing the results
Both lines have the **same slope** and the **same y-intercept** (\( y = 2x - 3 \)). This indicates that the lines are **coinciding**, meaning they are exactly the same line.

### Final Answer
The correct option is:
- **The graphs are coinciding.**

Would you like more details, or have any questions? Here are 5 related questions to deepen your understanding:

1. How can we determine if two linear equations are parallel, intersecting, or perpendicular?
2. What does it mean graphically when two lines coincide?
3. How do we calculate the slopes of two given linear equations?
4. What role does the y-intercept play in determining if two lines are identical?
5. How can systems of equations be solved using the elimination or substitution method?

**Tip:** To check if two lines are identical, compare both the slopes and the y-intercepts after converting to slope-intercept form.

Refer to the given systems of linear equation. Which of the following is TRUE about the graph of the given systems of linear equation?

This problem involves analyzing the system of linear equations 8x - 4y = 12 and -6x + 3y = -9 to determine if the graphs are coinciding, parallel, intersecting, or perpendicular. The correct answer shows that the lines are coinciding as both equations represent the same line.

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