Question

find the rate of change represented by the data in the table below.
x | -7 0 7 14 21
y | -1 2 5 8 11
is the rate of change positive or negative?
a) positive b) negative
rate of change: \\(\frac{\text{change in } y}{\text{change in } x}\\)

Explanation:

Step1: Calculate change in x

$\Delta x = 0 - (-7) = 7$

Step2: Calculate change in y

$\Delta y = 2 - (-1) = 3$

Step3: Compute rate of change

$\text{Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{3}{7}$

Step4: Sign of rate of change

Since $\frac{3}{7} > 0$, the rate is positive.

Answer:

Rate of Change: $\frac{3}{7}$
a) positive