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 the slope in any linear relation all we need is two points, let me rewrite this table some [tex]\begin{array}{|c|c|ll} \cline{1-2} x(h)&y(c)\\ \cline{1-2} 5&15\\ 8&24\\ 12&36\\ 24&72\\ \cline{1-2} \end{array}[/tex]
so from the table, let's use hmmm (8 , 24) and (24 , 72)
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{24})\qquad (\stackrel{x_2}{24}~,~\stackrel{y_2}{72}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{72}-\stackrel{y1}{24}}}{\underset{run} {\underset{x_2}{24}-\underset{x_1}{8}}}\implies \cfrac{48}{16}\implies 3[/tex]