For a given function, slope is defined as the change in outputs, or y-values divided by the change in inputs, or x-values. In essence the slope asks "For a given change in x, how much does y change?" or even more simply: "How steep is the graph of this function?". This can be represented mathematically by the formula: [tex]slope=m=\frac{rise}{run}=\frac{\Delta y}{\Delta x}-\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Substituting our known vlaues we have:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{2-0}{2-(-1)}[/tex]
[tex]m=\frac{2}{3}[/tex]
