For the straight line 3x + 2y = -12, find the exact point where it intersects the Y-axis. Recall that on the Y-axis, the x-coordinate is always 0, and then solve for y.

Introduction / Context: This question tests intercepts in coordinate geometry. The Y-intercept of a line is the point where the line crosses the Y-axis. Every point on the Y-axis has x = 0, so to find the Y-intercept you simply set x = 0 in the line’s equation and solve for y. This is a standard one-step substitution problem used frequently in aptitude and analytic geometry.

Given Data / Assumptions:

• Line equation: 3x + 2y = -12 • On Y-axis: x = 0 • Required: intersection point with Y-axis (x, y)

Concept / Approach: Y-intercept is found by substituting x = 0 and solving for y. The resulting point will have the form (0, y). Do not confuse it with the X-intercept, where y = 0 instead.

Step-by-Step Solution: 1) Start with the line: 3x + 2y = -12 2) Set x = 0 for the Y-axis: 3(0) + 2y = -12 3) Simplify: 2y = -12 4) Divide by 2: y = -6 5) So the Y-intercept point is: (0, -6)

Verification / Alternative check: Plug the point (0, -6) back into the equation: 3(0) + 2(-6) = -12, which matches the right side. Therefore, the point lies on the line and is indeed where x = 0, confirming it is the Y-intercept.

Why Other Options Are Wrong: • (0, 6): wrong sign for y. • (-4, 0) and (4, 0): these are X-intercept style points (y = 0), not Y-intercepts. • (0, -12): happens if you forget to divide by 2 after setting x = 0.

Common Pitfalls: • Confusing Y-intercept (x = 0) with X-intercept (y = 0). • Solving 2y = -12 but forgetting the final division by 2.

Final Answer: (0, -6)