Find the point where the line 2x - 3y = 6 intersects the y-axis by setting x = 0, and then choose the correct y-intercept coordinate.

Introduction / Context:
This coordinate geometry question asks you to find the y-intercept of a line given in standard form. The y-intercept is the point where the line cuts the y-axis, which is a very common requirement in graph based aptitude problems. Understanding how to find intercepts quickly from equations of lines is an essential skill for both exams and real life applications involving graphs.

Given Data / Assumptions:

• The equation of the line is 2x - 3y = 6.
• The y-axis corresponds to x = 0.
• The y-intercept is the point where the line crosses the y-axis.
• Coordinates are written in the form (x, y).

Concept / Approach:
To find where a line meets the y-axis, we simply set x = 0 in the equation, because all points on the y-axis have x coordinate equal to zero. Substituting x = 0 into the equation and solving for y gives the y coordinate of the intersection point. The resulting pair (0, y) is the y-intercept. This is a straightforward application of the definition of the axes in the Cartesian plane.

Step-by-Step Solution:
Start from the line equation: 2x - 3y = 6. For the y-axis, set x = 0. Substitute x = 0: 2(0) - 3y = 6, which simplifies to -3y = 6. Solve for y: y = 6 / (-3) = -2. Thus the line meets the y-axis at the point (0, -2).
Verification / Alternative check:
If you rewrite the equation in slope intercept form, you can verify the same result. From 2x - 3y = 6, isolate y to get -3y = -2x + 6 and then y = (2/3)x - 2. In this form, the constant term -2 represents the y-intercept directly, confirming that the line crosses the y-axis at (0, -2). This second method matches the result of the substitution method.

Why Other Options Are Wrong:
Option b (0, 2) has the correct x coordinate but the opposite sign for y, which would correspond to 2x - 3(2) = 2x - 6, not equal to 6 when x = 0. Options c and d, (-2, 0) and (2, 0), are x-intercepts rather than y-intercepts because they place the point on the x-axis. Option e (-3, 2) satisfies neither the y-axis condition nor the line equation correctly when substituted.

Common Pitfalls:
A common mistake is to mix up x and y intercepts and accidentally set y = 0 when asked for the y-intercept. Another pitfall is mishandling the algebraic signs when solving for y, especially when dividing by a negative coefficient. Carefully substituting x = 0 and then performing the division correctly avoids these issues.

Final Answer:
The line 2x - 3y = 6 cuts the y-axis at the point (0, -2).