What condition leads a linear equation to only pass through two quadrants?

A linear equation typically has the general form y = mx + b, where m is the slope and b is the y-intercept. The nature of the slope determines how the line crosses the Cartesian plane.

When a linear equation is parallel to the x-axis, it means that the slope (m) is zero. In this case, the equation takes the form of y = c, where c is a constant. Such a line runs horizontally and will extend infinitely in both the positive and negative directions on the x-axis while remaining constant in the y-value. This means the line only intersects the y-axis at one point, resulting in the line passing through two quadrants: the upper and lower quadrants depending on the value of c.

Conversely, if a linear equation is parallel to the y-axis, the slope is undefined, and the equation is of the form x = c. This results in a vertical line that only intersects two quadrants: the right and left quadrants based on the value of c.

In summary, a linear equation that is parallel to either the x-axis or the y-axis can only touch two quadrants at any given time, which makes this condition the appropriate answer.