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.
and to get it, we only need two points off a line, hmmm let's use those two points in the picture below.
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{4}}}\implies \cfrac{6}{4}\implies \cfrac{3}{2}[/tex]
