rise refers to the y coordinates(i.e y2 - y1) whereas the "run" refers to the x coordinates(i.e x2 - x1), hence the algebraic expression slope = rise/run or to put it mathematically, m = (y2 - y1)/(x2 - x1) or m = change in y/change in x.
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Rise/run is the slope of a line.
1" rise per every 12" run
This is plotted with a straight line. The "rise" is how far the line rises vertically. the "run" is how far it traverses horizontally. The division "rise" / "run" is the "slope" of the line.
Rise represents the change in y-values on a graph, e.g. if the rise is equal to 10, the y-value changes by 10. Run represents the change in x-values on a graph, e.g. if the run is equal to 5, the x-value changes by 5. knowing both the rise and the run is necessary to calculate the gradient, or slope of a graph - this is done by dividing the rise by the run, in this case it would be equal to 10/5 = 2
Slope is the ratio of rise to run. Meaning: rise is the change in y value (height, rise). Run is the change in x value (run). It is calculated as (y2-y1)/(x2-x1). It is often represented by the letter m. Y-intercept is the y value at which your curve crosses the y-intercept. Put another way, it's the y-value when x=0 (the y-axis). Hope this helps.