Question

Find the constant rate of change for each table

Answer 1

the constant rate of change, or average rate of change, is just its slope, so we can just pick any two points to get it.

$\bf \begin{array}{|cc|ll}\cline{1-2}\stackrel{x}{time}&\stackrel{y}{distance}\\\cline{1-2}1&6\\\underline{2}&\underline{12}\\3&18\\\underline{4}&\underline{24}\\\cline{1-2}\end{array}~\hspace{7em}\begin{array}{llll}(\stackrel{x_1}{2}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{24})\\\\\\slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{24-12}{4-2}\\\\\\\cfrac{12}{2}\implies 6\end{array}$

Answer 2

The constant rate of change for the table is 6m per 1s.

The constant rate of change exists in linear mathematical relationships and is simply given as the slope.

In this scenario, the rate of change is given as;

• Slope = rate of change = (D2 - D1)/(t2 -t1).

• This constant rate of change can also be evaluated by picking data points: 3 and 4.

Ultimately, the constant rate of change is;

• Rate of change = (12-6)/(2-1).

Rate of change = 6m per 1s.

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