Question

Describe the relationship between the following linear equation and the given inequality.2x−3y=6

A) The equation and inequality represent parallel lines.
B) The equation and inequality represent perpendicular lines.
C) The equation and inequality represent the same line.
D) The equation and inequality have no relationship.

Answer 1

The linear equation and inequality have no relationship.

Step-by-step explanation:

The relationship between the linear equation and the given inequality can be determined by analyzing their slopes and y-intercepts.

The linear equation 2x - 3y = 6 is in standard form, where the slope can be found by rearranging the equation to y = mx + b form.

In this case, the slope is 2/3, which indicates a positive slope. On the other hand, an inequality has an inequality symbol (<, >, ≤, ≥) and does not represent a specific line, but rather a region of solutions.

Therefore, the correct relationship between the linear equation and inequality is that they have no relationship (option D).