Question

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

x	y
14	20
15	10
16	0

linear
nonlinear

Explanation:

Step1: Calculate the rate of change between the first two points

The formula for the rate of change (slope) 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 \((14, 20)\) and \((15, 10)\), we have \(x_1 = 14\), \(y_1 = 20\), \(x_2 = 15\), \(y_2 = 10\). So the slope \(m_1=\frac{10 - 20}{15 - 14}=\frac{- 10}{1}=- 10\).

Step2: Calculate the rate of change between the second and third points

For the points \((15, 10)\) and \((16, 0)\), we have \(x_1 = 15\), \(y_1 = 10\), \(x_2 = 16\), \(y_2 = 0\). So the slope \(m_2=\frac{0 - 10}{16 - 15}=\frac{- 10}{1}=- 10\).

Step3: Compare the slopes

Since \(m_1=m_2=- 10\) (the rate of change is constant), the function is linear.

Answer:

linear