In a graph, what does rise over run equal?

Question

Genesis Allen · Accepted Answer

In a word 'slope'. To be more specific, 'average slope'.

If a straight line passes through two points #(x_1, y_1)# and #(x_2, y_2)# where #x_2 > x_1#. then the run is #(x_2 - x_1)#, the rise is #(y_2 - y_1)# and the slope #m# of the line is defined as: #m = (Delta y)/(Delta x) = # run / rise #= (y_2 - y_1)/(x_2 - x_1) # If instead of a straight line, we have a function #f(x)# which is continuous and otherwise well-behaved over the interval #[x_1, x_2]# and #f(x_1) = y_1# and #f(x_2) = y_2# then the average slope of #f(x)# over the interval #[x_1, x_2]# is also #m = (y_2 - y_1)/(x_2 - x_1)# If you are familiar with the terminology, we are basically evaluating the integral of the derivative of #f(x)# over the interval #[x_1, x_2]#, then dividing by the length of the interval. This is like adding up the slopes at each point and dividing by the number of measurements to get the average.

Eva Adamson · Answer

undefined In a graph, "rise over run" refers to the ratio of the vertical change (rise) to the horizontal change (run) between two points on the graph. It represents the slope of the line connecting the two points.