Question

Find the the slope of the line passing through points 2,2 and -1,0

Answer 1

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: $slope=m=\frac{rise}{run}=\frac{\Delta y}{\Delta x}-\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting our known vlaues we have:
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
$m=\frac{2-0}{2-(-1)}$
$m=\frac{2}{3}$