Question

average rate of change
between two points $(x_1,y_1)$ and $(x_2,y_2)$
$\frac{y_2 - y_1}{x_2 - x_1}$

1. use the table to determine the average rate of change from

$x=-3$ to $x = 6$.
a. write the ordered pairs:
$(-3,8)$ and $(6,62)$
b. substitute values and simplify:
avg rate $=\frac{62 - 8}{6-(-3)}=\frac{54}{9}=6$

1. use the graph to determine the

average rate of change from
$x=-5$ to $x=-1$?
a. write the ordered pairs:
$(),()$ and $(),()$
b. substitute values and simplify:
avg rate $=\frac{-}{-}$

Explanation:

Step1: Identify ordered pairs from the graph

From the graph, when \(x = - 5\), \(y = 8\) (the first point \((-5,8)\)); when \(x=-1\), \(y = 0\) (the second point \((-1,0)\))

Step2: Use the average rate of change formula

The formula for the average rate of change between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1=-5,y_1 = 8,x_2=-1,y_2 = 0\) into the formula:

$$
LATEXBLOCK0
$$

Answer:

a. \((-5,8)\) and \((-1,0)\)
b. \(\frac{0 - 8}{-1-(-5)}=-2\)