Question

find the rate of change represented by the data in the table below.
x|-14 -7 0 7 14
y|1 -1 -3 -5 -7
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: Pick two data pairs

Choose $(x_1,y_1)=(-14,1)$ and $(x_2,y_2)=(-7,-1)$

Step2: Calculate change in y

$\Delta y = y_2 - y_1 = -1 - 1 = -2$

Step3: Calculate change in x

$\Delta x = x_2 - x_1 = -7 - (-14) = 7$

Step4: Compute rate of change

$\text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{-2}{7}$

Step5: Sign of rate of change

$\frac{-2}{7}$ is less than 0, so negative.

Answer:

Rate of change: $\boldsymbol{\frac{-2}{7}}$
b) negative