Chapter 3.2, Problem 51E

To determine

Whether the function represented by the ordered pairs $\left(0,2\right)$ , $\left(3,14\right)$ , $\left(5,22\right)$ , $\left(9,38\right)$ , $\left(11,46\right)$ linear or non-linear.

Answer to Problem 51E

Linear

Explanation of Solution

Given:

The function with ordered pairs is $\left(0,2\right)$ , $\left(3,14\right)$ , $\left(5,22\right)$ , $\left(9,38\right)$ , $\left(11,46\right)$ .

Concept Used:

Slope between the point $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is:

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

A linear function is a function with constant rate of change, that is constant slope.

So, to determine that if the function represented by the ordered pairs $\left(0,2\right)$ , $\left(3,14\right)$ , $\left(5,22\right)$ , $\left(9,38\right)$ , $\left(11,46\right)$ linear or non-linear, determine the slope between each of the given points.

Slope between $\left(0,2\right)$ and $\left(3,14\right)$

  $=\frac{14-2}{3-0}=\frac{12}{3}=4$

Slope between $\left(3,14\right)$ and $\left(5,22\right)$

  $=\frac{22-14}{5-3}=\frac{8}{2}=4$

Slope between $\left(5,22\right)$ and $\left(9,38\right)$

  $=\frac{38-22}{9-5}=\frac{16}{4}=4$

Slope between $\left(9,38\right)$ and $\left(11,46\right)$

  $=\frac{46-38}{11-9}=\frac{8}{2}=4$

Slope between each point is 4, thus the function represented by the given ordered pairs is linear.