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]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{5})~\hspace{10em} \stackrel{slope}{m}\implies 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{5}(x-\stackrel{x_1}{2}) \\\\\\ y-5=5x-10\implies y = 5x-5[/tex]
