Use the given graph to determine whether the line has positive slope, negative slope, or zero sl

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Use the given graph to determine whether the line has...

Key Concepts

Slope

Slope is a measure of the steepness of a line, defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. It indicates how much the line tilts and is fundamental in understanding linear relationships in coordinate geometry.

Positive Slope

A line with a positive slope rises as it moves from left to right, indicating that as the x-values increase, the y-values also increase. This is representative of a direct relationship between the two variables in many mathematical contexts.

Negative Slope

A line with a negative slope falls as it moves from left to right, meaning that as the x-values increase, the y-values decrease. This inverse relationship is common in various applications, particularly in scenarios where one variable tends to decrease when the other increases.

Zero Slope

A line with a zero slope is horizontal, showing no rise or fall as it extends across the graph. This implies there is no change in the y-values regardless of variations in the x-values, representing a constant relationship between the two variables.

Undefined Slope

An undefined slope is observed in vertical lines, where the x-value remains constant and the concept of 'rise over run' cannot be applied because the run is zero. This characteristic makes the slope undefined, which is a unique case in understanding the behavior of lines on a graph.

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