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!