Find the exact area (in square units) of the triangle formed by the line 2x − 3y + 6 = 0 together with the coordinate axes.

Introduction / Context:
Lines that intersect the coordinate axes form a right triangle with the axes. The area of this triangle is 1/2 * |x-intercept| * |y-intercept|. We will find intercepts of 2x − 3y + 6 = 0 and compute the area using absolute values of those intercept lengths.

Given Data / Assumptions:

• Line: 2x − 3y + 6 = 0.
• Intercepts are taken with respect to the x- and y-axes.

Concept / Approach:
Set y = 0 to get the x-intercept, and set x = 0 to get the y-intercept. The triangle with axes has legs equal to the magnitudes of these intercepts. Then area = (1/2) * |x-intercept| * |y-intercept|.

Step-by-Step Solution:

Verification / Alternative check:
Convert to intercept form: x/(−3) + y/2 = 1. Using absolute intercepts, area = (1/2)*3*2 = 3, consistent with the above method.

Why Other Options Are Wrong:

• 1.5 sq. units, 6 sq. units, 9 sq. units: These do not match the product of legs divided by 2 for the given intercepts. “3 sq. units 2” is malformed.

Common Pitfalls:

• Using the signed intercept (−3) directly without taking absolute value for length.
• Confusing slope-intercept form with intercept computation.

Final Answer:
3 sq. units