Conquer ALEKS 2025 – Max Your Knowledge Spaces with Ease!

The standard form of a linear equation is typically expressed as Ax + By = C, where A, B, and C are integers, and A and B cannot both be zero at the same time. This definition ensures that the equation represents a valid line in a two-dimensional space.

When considering the first choice, stating that both A and B are zero leads to the equation 0x + 0y = C, which simplifies to 0 = C. This scenario is problematic because it does not represent a line. Specifically, if C equals 0, it suggests that there are infinitely many points (i.e., every point in the plane) that satisfy this equation, effectively not yielding a linear relationship. If C is not equal to zero, the equation indicates a contradiction and has no solution at all. Therefore, having both A and B as zero does not constitute a valid standard form equation.

In contrast, the other options maintain the requirement for standard form: they allow for A or B to be zero but not both simultaneously. Moreover, they ensure that the equation can indeed describe a line in a meaningful way. For instance, having either A or B as a negative value or ensuring that A and B are both not zero contributes to the equation