The equation you provided is a linear equation in two variables, $x$ and $y$. You can approach solving or analyzing this equation in several ways, such as:

1. Rearrange into Slope-Intercept Form:

To write the equation in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept: $3x - 2y = 6$ Solve for $y$: $-2y = -3x + 6$ $y = \frac{3}{2}x - 3$ Now, the equation is in the form $y = \frac{3}{2}x - 3$, where the slope $m = \frac{3}{2}$ and the y-intercept is $-3$.

2. Find the Intercepts:

• To find the x-intercept, set $y = 0$ and solve for $x$: $3x - 2(0) = 6 \quad \Rightarrow \quad 3x = 6 \quad \Rightarrow \quad x = 2$ So the x-intercept is $(2, 0)$.

• To find the y-intercept, set $x = 0$ and solve for $y$: $3(0) - 2y = 6 \quad \Rightarrow \quad -2y = 6 \quad \Rightarrow \quad y = -3$ So the y-intercept is $(0, -3)$.

Would you like a deeper explanation of one of these methods or a graphical representation of the equation?

Related Questions:

1. How do you graph a line from an equation?
2. What is the meaning of slope and intercept in linear equations?
3. How do you convert any linear equation to slope-intercept form?
4. What are parallel and perpendicular lines, and how are they related to slopes?
5. Can you explain how to solve systems of linear equations?

Tip:

To quickly find intercepts, set the opposite variable to zero and solve. This provides key points to help graph the line easily.