Explain how rise over run is relating to change in y over change in x?

Answer 1

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.