Question

find the rate of change represented by the data in the table below.
\

$$\begin{array}{c|ccccc}x&-16&-8&0&8&16\\\\y&-9&-2&5&12&19\\end{array}$$

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

Explanation:

Step1: Calculate change in y and x

Take two points, e.g., (-16, -9) and (-8, -2).
Change in \( y = -2 - (-9) = 7 \)
Change in \( x = -8 - (-16) = 8 \)

Step2: Find rate of change

Rate of change \( = \frac{\text{change in } y}{\text{change in } x} = \frac{7}{8} \).
Check sign: \( \frac{7}{8} > 0 \), so positive.

Answer:

a) positive