Question

find the rate of change represented by the data in the table below.
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$$\begin{array}{c|ccccc}x&0&5&10&15&20\\hline y&0&2&4&6&8\\end{array}$$

is the rate of change positive or negative?
a) positive \t\t b) negative
rate of change: \frac{\text{change in } y}{\text{change in } x}

Explanation:

Step1: Calculate change in y

$\Delta y = 2 - 0 = 2$

Step2: Calculate change in x

$\Delta x = 5 - 0 = 5$

Step3: Compute rate of change

$\text{Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{2}{5} = 0.4$

Step4: Determine sign of rate

The value $0.4$ is greater than 0, so it is positive.

Answer:

Rate of Change: $\frac{2}{5}$ (or 0.4)
a) positive