Final Answer:
The method closest to determining the proximity of the point (-3, -2) to the line 6x + 5y - 6 = 0 is (Option B) Distance Formula.
Step-by-step explanation:
To find the closest point on a line to an external point, the Distance Formula is often employed. Given the line 6x + 5y - 6 = 0, we can consider it as the equation of a plane in the xy-coordinate system. The distance between this line and the point (-3, -2) can be found using the Distance Formula, where A, B, and C are coefficients from the equation of the line. In this case, A = 6, B = 5, and C = -6 (Option B).
The Distance Formula calculates the perpendicular distance from the point to the line, providing a straightforward approach to determining proximity. Linear Inequalities (Option A) and Systems of Inequalities (Option C) are not applicable in this context as the question is about proximity to a specific point rather than satisfying inequalities. Quadratic Inequalities (Option D) are also not relevant in this linear scenario.
In conclusion, the Distance Formula is the appropriate method to determine the distance from the point (-3, -2) to the line 6x + 5y - 6 = 0. This application showcases the practicality of mathematical tools in analyzing spatial relationships and is fundamental in various fields, including geometry and optimization problems.