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the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{64})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{96}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{96}-\stackrel{y1}{64}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{4}}}\implies \cfrac{\stackrel{bottles}{32}}{\underset{mins}{2}}\implies \cfrac{\stackrel{bottles}{16}}{\underset{mins}{1}}[/tex]
Answer:
Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).