If a linear function has a slope of -2, what does that imply about the graph of the function?

When a linear function has a slope of -2, it indicates that for every unit increase in the x value, the y value decreases by 2 units. This negative slope implies that as you move from left to right along the x-axis, the graph of the function will fall.

This behavior is characteristic of functions with negative slopes, where the height of the graph decreases as the x-coordinate increases. The steeper the slope, in this case, the more quickly the graph will decline; a slope of -2 suggests a relatively steep downward trend.

In contrast, a positive slope would indicate that the graph rises as x increases, while a zero slope would signify a horizontal line, and an undefined slope (typically associated with vertical lines) would mean that the x value remains constant regardless of the y value. Therefore, a slope of -2 clearly indicates that as x increases, the y value falls, affirming that the graph of this linear function falls as x increases.