Question

The table shows the linear function f.

Answer 1

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.

`\bf \begin{array}l \cline{1-6} \qquad x\qquad &-6&-5&-4&-3&-2\\ \cline{1-6} f(x)&22&19&16&13&10\\ \cline{1-6} \end{array}~\hfill \stackrel{\textit{interval where }x ~\in~ [-5,-2]}{(\stackrel{x_1}{-5}~,~\stackrel{y_1}{19})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{10})} \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{19}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{(-5)}}}\implies \cfrac{-9}{-2+5}\implies \cfrac{-9}{3}\implies -3`