Find the \( y \)-intercept of the line given by \( 2x - 3y = 6 \).

["# Find the ( y )-Intercept of the Line Given by ( 2x - 3y = 6 )", "Understanding the ( y )-intercept of a line is key in algebra and coordinate geometry. The ( y )-intercept is the point where the line crosses the ( y )-axis, which occurs when ( x = 0 ). In this article, we’ll walk through how to find the ( y )-intercept of the line represented by the equation:", "[\n2x - 3y = 6\n]", "## Step-by-Step: How to Find the ( y )-Intercept", "### Step 1: Set ( x = 0 ) in the equation\nTo find the ( y )-intercept, substitute ( x = 0 ) into the line equation:", "[\n2(0) - 3y = 6\n]", "Simplifying:", "[\n-3y = 6\n]", "### Step 2: Solve for ( y )\nDivide both sides by (-3):", "[\ny = \frac{6}{-3} = -2\n]", "### Step 3: Write the intercept as an ordered pair\nThe point where ( x = 0 ) and ( y = -2 ) is ((0, -2)). This is the ( y )-intercept.", "---", "### Final Answer\nThe ( y )-intercept of the line ( 2x - 3y = 6 ) is:", "[\n\boxed{(0,\ -2)}\n]", "---", "## Why Knowing the ( y )-Intercept Matters", "The ( y )-intercept provides important information about the line’s position relative to the axes. For graphing, it serves as a starting point when plotting the line. In real-world applications, it can represent initial values—such as starting balance, starting price, or baseline measurement—when the independent variable (( x )) is zero.", "Mastering how to find the ( y )-intercept is essential for solving equations, interpreting graphs, and applying linear relationships in science, economics, and engineering.", "---", "If you’re studying for exams or working through linear equations, remember:\nSet ( x = 0 ), solve for ( y ), and that’s your ( y )-intercept!\nStay confident—every intercept tells a story on the graph."]