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The equation given is \( 6x - 5y = -30 \), and we are tasked with matching the equation to one of the four graphs labeled [A], [B], [C], and [D].

### Step 1: Convert the Equation into Slope-Intercept Form
We will first convert the equation into the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Start with the equation:
\[
6x - 5y = -30
\]
Solve for \( y \):
\[
-5y = -6x - 30
\]
Divide by -5:
\[
y = \frac{6}{5}x + 6
\]

Thus, the slope-intercept form is:
\[
y = \frac{6}{5}x + 6
\]
Here, the slope is \( \frac{6}{5} \) and the y-intercept is 6.

### Step 2: Analyze the Graph
- The slope \( \frac{6}{5} \) means that the line rises 6 units for every 5 units it moves to the right.
- The y-intercept is 6, which means the line crosses the y-axis at \( (0, 6) \).

### Step 3: Match with the Graphs
- [A]: This graph shows a negative slope, which is incorrect.
- [B]: This graph shows a positive slope, and the y-intercept appears to be at \( (0, 6) \), which matches our equation. This is likely the correct graph.
- [C] and [D]: These graphs do not have the correct slope or intercept for our equation.

### Conclusion:
The correct answer is **[B]**.

Would you like further details or have any questions? Here are some related questions to explore:

1. How do we determine the slope from an equation in standard form?
2. What is the significance of the y-intercept in a linear equation?
3. How would the graph change if the slope were negative?
4. How can we quickly convert from standard form to slope-intercept form?
5. What methods can be used to graph a line if slope-intercept form isn't used?

**Tip**: Always check the slope and y-intercept when matching an equation to a graph—it helps you quickly rule out incorrect options.

Determine which graph corresponds to the equation 6x - 5y = -30.

Learn how to graph the linear equation 6x - 5y = -30 by converting it to slope-intercept form and identifying the correct graph. This problem explains key concepts like slope and y-intercept. Suitable for students in Grades 9-10.

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