To solve the linear equation \(3x - 4y = 6\), we can approach it in different ways depending on what you're looking for. I'll assume you're interested in solving for one variable in terms of the other (either \(x\) or \(y\)).

### Solving for \(x\) in terms of \(y\):
1. Start with the given equation:
   \[
   3x - 4y = 6
   \]
2. Add \(4y\) to both sides:
   \[
   3x = 6 + 4y
   \]
3. Divide both sides by 3 to solve for \(x\):
   \[
   x = \frac{6 + 4y}{3}
   \]
   Simplifying:
   \[
   x = 2 + \frac{4y}{3}
   \]

### Solving for \(y\) in terms of \(x\):
1. Start with the same equation:
   \[
   3x - 4y = 6
   \]
2. Subtract \(3x\) from both sides:
   \[
   -4y = 6 - 3x
   \]
3. Divide both sides by \(-4\):
   \[
   y = \frac{3x - 6}{4}
   \]
   Simplifying:
   \[
   y = \frac{3x}{4} - \frac{6}{4}
   \]
   \[
   y = \frac{3x}{4} - \frac{3}{2}
   \]

Would you like more details or have any questions?

Here are 5 questions for further practice:
1. What is the slope of the line represented by \(3x - 4y = 6\)?
2. How do you graph the equation \(3x - 4y = 6\)?
3. What is the solution to the system of equations \(3x - 4y = 6\) and \(x + y = 5\)?
4. How do you rewrite \(3x - 4y = 6\) in slope-intercept form?
5. Can you find the intercepts of the line \(3x - 4y = 6\)?

**Tip**: When solving linear equations, always isolate the variable by performing inverse operations step-by-step.

Learn how to solve the linear equation 3x - 4y = 6, including solving for x in terms of y and vice versa. This problem focuses on algebraic manipulation and key concepts in linear equations. Suitable for students in Grades 8-10.

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