The equation \(3x - 4y = 6\) represents a linear equation in two variables, \(x\) and \(y\). There are different ways to handle this equation depending on what you're looking to find:

### 1. **Solving for One Variable:**
If you want to express one variable in terms of the other, you can solve for \(y\) or \(x\).

**Solving for \(y\):**
\[
3x - 4y = 6
\]
Subtract \(3x\) from both sides:
\[
-4y = -3x + 6
\]
Divide by \(-4\):
\[
y = \frac{3x - 6}{4} = \frac{3x}{4} - \frac{6}{4} = \frac{3x}{4} - \frac{3}{2}
\]

**Solving for \(x\):**
\[
3x - 4y = 6
\]
Add \(4y\) to both sides:
\[
3x = 4y + 6
\]
Divide by \(3\):
\[
x = \frac{4y + 6}{3} = \frac{4y}{3} + 2
\]

### 2. **Finding the Intercepts:**
You can also find the intercepts of the line represented by this equation.

**x-intercept (when \(y = 0\)):**
\[
3x - 4(0) = 6 \implies 3x = 6 \implies x = 2
\]
So, the x-intercept is \( (2, 0) \).

**y-intercept (when \(x = 0\)):**
\[
3(0) - 4y = 6 \implies -4y = 6 \implies y = -\frac{3}{2}
\]
So, the y-intercept is \( (0, -\frac{3}{2}) \).

### 3. **Graphing the Equation:**
To graph the equation, you can plot the intercepts \((2, 0)\) and \((0, -\frac{3}{2})\) on a coordinate plane and draw a line through these points.

Would you like more details on any of these steps or have any questions?

Here are 5 related questions:
1. How do you find the slope of a line given its equation?
2. Can you solve for \(y\) in terms of \(x\) and then graph the equation?
3. What are the steps to graph a line given its standard form equation?
4. How can you determine if two lines are parallel or perpendicular?
5. How would you find the intersection point of two lines?

**Tip:** When solving for a variable, make sure to simplify the equation as much as possible for easier interpretation!

Learn how to solve the linear equation 3x - 4y = 6 with a detailed step-by-step solution. This problem covers key algebraic concepts such as linear equations, finding intercepts, and graphing. Suitable for students in Grades 7-9.

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