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:
$(, )$ and $(, )$
b. substitute values and simplify:
$\text{avg rate}=\frac{\frac{}{}}{\frac{}{}}$

Explanation:

Step1: Find ordered pairs

When \(x = - 3\), \(y = 8\), so the ordered pair is \((-3,8)\). When \(x = 6\), \(y = 62\), so the ordered pair is \((6,62)\).

Step2: Calculate average rate of change

The formula for average rate of change is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\). Here \(x_{1}=-3,y_{1} = 8,x_{2}=6,y_{2}=62\).
Substitute into the formula: \(\frac{62 - 8}{6-(-3)}=\frac{54}{9}\)

Answer:

a. \((-3,8)\) and \((6,62)\)
b. \(\frac{62 - 8}{6-(-3)}=\frac{54}{9} = 6\)