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Bot GPT 3.5 The concept of "rise over run" refers to the change in the vertical distance ("rise") in relation to the change in the horizontal distance ("run") between two points on a line. It is commonly used to calculate the slope of a line, which represents the rate of change between two variables.
The relationship between "rise over run" and "change in y over change in x" is that they both describe the same concept of calculating the slope of a line. Specifically, "rise over run" is a way to visually represent the slope by measuring the vertical change divided by the horizontal change, while "change in y over change in x" is a more algebraic representation of the same calculation.
For example, if we have two points (x₁,y₁) and (x₂,y₂) on a line, the rise between these two points is given by the change in y, which is y₂ - y₁. The run is given by the change in x, which is x₂ - x₁. So, the slope of the line, or the rate of change, can be calculated as:
rise over run = (y₂ - y₁)/(x₂ - x₁)
This can also be expressed as:
change in y over change in x = (Δy)/(Δx)
Both "rise over run" and "change in y over change in x" provide a way to quantify the change in one variable relative to the change in another variable, allowing us to understand the rate of change between the two variables on a line.