Question

the table shows a function. is the function linear or nonlinear?

x	y
-9	20
5	6
12	-1

options: linear, nonlinear

Explanation:

Step1: Calculate the slope between the first two points

The formula for slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For the points $(-9, 20)$ and $(5, 6)$:
$m_1 = \frac{6 - 20}{5 - (-9)} = \frac{-14}{14} = -1$

Step2: Calculate the slope between the second and third points

For the points $(5, 6)$ and $(12, -1)$:
$m_2 = \frac{-1 - 6}{12 - 5} = \frac{-7}{7} = -1$

Step3: Check if slopes are equal

Since $m_1 = m_2 = -1$, the rate of change is constant. A function with a constant rate of change is linear.

Answer:

linear