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.