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The formula m= V2 - V1 X2 - X1

The product of these slopes is This product shows that the slopes are negative reciprocals. It is given that the lines are perpendicular and we have shown that the slopes of the lines are negative reciprocals.

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Final answer:

Perpendicular lines have slopes that are negative reciprocals, meaning the product of their slopes is -1. Slope calculations and relationships are critical in understanding how graphs behave and how variables are interconnected.

Step-by-step explanation:

The concept in question pertains to the characteristics of slopes in coordinate geometry, specifically pertaining to the slopes of perpendicular lines. The slope, denoted by 'm', is a measure of how steep a line is and is calculated by the formula m = (V2 - V1)/(X2 - X1).

A negative slope indicates a line that falls as it moves from left to right, representing a negative relationship between x and y, such as the altitude-air density relationship or the inverse relationship between price and quantity demanded.

Perpendicular lines have slopes that are negative reciprocals of each other. This means that if one line has a slope of 'a', the perpendicular line will have a slope of '-1/a'. The product of the slopes of two perpendicular lines is -1, confirming this distinctive relationship.

Moreover, comparing the slope to the general linear equation y = mx + b, where 'm' is the slope, we note that slopes are essential for understanding the graph's behavior and can be related to other formulas, such as -ΔH°/R in certain contexts.

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