In coordinate geometry, consider the straight line given by the equation 3x + 2y = 12. At which coordinate point does this line intersect and cut the Y axis?

Introduction / Context:
Finding intercepts of a line is a basic skill in coordinate geometry. The Y intercept is the point where the line crosses the Y axis, and it is found by setting x equal to zero. This question checks whether you are comfortable with this standard technique.

Given Data / Assumptions:

• Equation of the line: 3x + 2y = 12.
• Y axis is defined by x = 0.
• We need the point where the line meets the Y axis.

Concept / Approach:
The Y intercept is the point on the line where x equals zero. Substituting x = 0 into the line equation and solving for y gives the Y intercept. This is a very fast method and is often used for sketching graphs of linear equations.

Step-by-Step Solution:
Start with 3x + 2y = 12. At the Y axis, x = 0, so substitute x = 0 into the equation. Then 3 * 0 + 2y = 12 gives 2y = 12. Divide both sides by 2 to get y = 6. So the point of intersection with the Y axis is (0, 6).
Verification / Alternative check:
You can also rewrite the equation in slope intercept form: 2y = 12 − 3x, so y = 6 − (3 / 2) x. When x = 0, y = 6, confirming the Y intercept is (0, 6).

Why Other Options Are Wrong:
Option b (0, −6) has the wrong sign of y. Option c (6, 0) and option d (−6, 0) are X intercept candidates, not Y intercepts. Option e (2, 3) lies on the line but does not correspond to x = 0, so it is not the Y intercept.

Common Pitfalls:
Students sometimes mix up X and Y intercepts, or they try to solve the equation for both variables unnecessarily. Always remember that for the Y intercept, x is zero, and for the X intercept, y is zero. This small reminder saves time and avoids confusion.

Final Answer:
The line 3x + 2y = 12 cuts the Y axis at the point (0, 6).