Question

ian was asked to create a table of values that had a rate of change of $-\frac{17}{11}$. he created the table below. did ian create the table correctly?

x	y
-22	8
-11	-9
0	-26

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\). We'll check the rate of change between consecutive points in the table.

Step2: Calculate rate between first and second point

First point: \((-22, 8)\), second point: \((-11, -9)\).
Slope \(m_1=\frac{-9 - 8}{-11 - (-22)}=\frac{-17}{11}=-\frac{17}{11}\).

Step3: Calculate rate between second and third point

Second point: \((-11, -9)\), third point: \((0, -26)\).
Slope \(m_2=\frac{-26 - (-9)}{0 - (-11)}=\frac{-17}{11}=-\frac{17}{11}\).

Answer:

Yes, Ian created the table correctly because the rate of change between consecutive points is \(-\frac{17}{11}\).