How many quadrants does a linear equation pass through if it has both an x-intercept and a y-intercept?

A linear equation with both an x-intercept and a y-intercept will cross the x-axis at some point and the y-axis at another. Since a linear equation can be represented geometrically as a straight line, its exact behavior depends on the signs of its slope.

When the line has both intercepts:

1. The x-intercept indicates where the line crosses the x-axis, which can occur in either the first quadrant (positive x and y) or the third quadrant (negative x and y) if extended in both directions.

2. The y-intercept signifies where the line crosses the y-axis, which can occur in the first quadrant (positive x and y) or the fourth quadrant (positive x, negative y).

Because the line will extend infinitely in both directions, it will inevitably pass through three distinct quadrants. For instance, if the line descends from the second quadrant, it crosses the y-axis while being in the second quadrant, then falls into the fourth quadrant and eventually crosses to the third quadrant if it is steeper than 45 degrees. If it has a gentle slope and rises from the third quadrant through the y-intercept, it will reach both the first and the second quadrant.

Therefore, it's essential that the line