A negative y-intercept in a linear equation indicates that the point where the line crosses the y-axis is below the origin (0, 0). In the context of the equation of a line, (y = mx + b), the y-intercept is represented by (b).

Here's a step-by-step explanation:

Understanding the y-intercept: The y-intercept is the value of (y) when (x = 0). It represents the point at which the line crosses the y-axis.

Negative y-intercept: When the y-intercept ((b)) is negative, it means that the point at which the line crosses the y-axis is below zero. For example, in the equation (y = 2x - 3), the y-intercept is (-3). This means the line crosses the y-axis at the point (0, -3).

Graphical interpretation: On a graph, this means that the initial value of (y) (when there is no (x) contribution) is less than zero. Graphically, the line starts at a point below the horizontal x-axis.

Real-world context: In a real-world situation, a negative y-intercept might indicate a starting deficit, loss, or decrease. For example, if the equation describes profit over time, a negative y-intercept could mean that there is an initial loss or cost.

Summary: Overall, a negative y-intercept just indicates that the starting point or initial value, represented by the line's crossing of the y-axis, is below zero on a Cartesian plane.

This understanding is useful for interpreting linear relationships, especially in analyzing and predicting data trends.

How is this relationship useful for interpreting linear relationships?