To find the $y$-intercept, set $x = 0$ in the equation of the line $3x - 2y = 6$ and solve for $y$:

["How to Find the Y-Intercept: A Step-by-Step Guide Using $3x - 2y = 6$", "Finding the $y$-intercept is an essential skill in algebra, essential not only for graphing linear equations but also for understanding key properties of lines. The $y$-intercept is the point where the line crosses the $y$-axis — this occurs when the value of $x$ is 0. In this article, we’ll learn how to find the $y$-intercept of the line given by the equation $3x - 2y = 6$, using the straightforward method of substitution.", "### What Is the Y-Intercept?", "The $y$-intercept is the value of $y$ when $x = 0$. Graphically, it’s the point $(0, b)$ on the coordinate plane, where $b$ is the $y$-intercept value. Determining this point helps us quickly plot linear equations and understand their behavior in real-world applications like economics, physics, and data analysis.", "### Solving for the Y-Intercept: Step-by-Step", "To find the $y$-intercept of the equation $3x - 2y = 6$, follow these steps:", "Step 1: Substitute $x = 0$ into the equation\nSince the $y$-intercept happens when $x = 0$, replace $x$ with 0:\n[\n3(0) - 2y = 6\n]", "Step 2: Simplify the equation\nThis simplifies to:\n[\n-2y = 6\n]", "Step 3: Solve for $y$\nTo isolate $y$, divide both sides by $-2$:\n[\ny = \frac{6}{-2} = -3\n]", "### The Result", "Therefore, the $y$-intercept of the line $3x - 2y = 6$ is at the point $(0, -3)$. This means the line crosses the $y$-axis at $-3$ on the vertical axis.", "### Why This Method Matters", "Using substitution is efficient because it transforms the equation from a general form into a simple linear equation in $y$, making it easy to solve. This method applies to any linear equation in two variables and is foundational for more complex algebraic and graphing techniques.", "---", "Conclusion", "Finding the $y$-intercept by setting $x = 0$ is a fundamental step in analyzing linear equations. For the line $3x - 2y = 6$, we determined the $y$-intercept is $-3$ through clear substitution and algebra. Mastering this approach strengthens your ability to interpret and graph equations, setting a strong foundation in mathematics.", "---", "*Keywords: Y-intercept, solving linear equations, $3x - 2y = 6$, graphing lines, algebra tutorial, intercept calculation, coordinate geometry."]