Determine whether the table represents a *linear* or *nonlinear* function.

$x$x​

$5$5​

$7$7​

$9$9​

$11$11​

$y$y​

$-9$−9​

$-3$−3​

$-1$−1​

$3$3​

The relation is a linearnonlinear function.

To determine whether the table represents a linear or nonlinear function, we can check the rate of change (also known as the slope) between consecutive pairs of points. A linear function will have a constant rate of change (slope), while a nonlinear function will not.

The points given are:

- (5, -9)
- (7, -3)
- (9, -1)
- (11, 3)

### Step 1: Calculate the change in $ y $ and $ x $ between consecutive points.

For the first pair of points, (5, -9) and (7, -3):
- Change in $ x $: $ 7 - 5 = 2 $
- Change in $ y $: $ -3 - (-9) = -3 + 9 = 6 $
- Slope: $ \frac{6}{2} = 3 $

For the second pair of points, (7, -3) and (9, -1):
- Change in $ x $: $ 9 - 7 = 2 $
- Change in $ y $: $ -1 - (-3) = -1 + 3 = 2 $
- Slope: $ \frac{2}{2} = 1 $

For the third pair of points, (9, -1) and (11, 3):
- Change in $ x $: $ 11 - 9 = 2 $
- Change in $ y $: $ 3 - (-1) = 3 + 1 = 4 $
- Slope: $ \frac{4}{2} = 2 $

### Step 2: Check if the slope is constant.
The slopes calculated are:
- $ 3 $ between the first pair,
- $ 1 $ between the second pair, and
- $ 2 $ between the third pair.

Since the slopes are not consistent, the rate of change is not constant. Therefore, **the function is nonlinear**.

---

Do you want more details on how the slope works, or do you have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you find the slope of a line between two points?
2. What is the geometric interpretation of a linear function?
3. How can you use a table to determine if a function is linear or nonlinear?
4. What are some characteristics of nonlinear functions?
5. Can a function be linear over a certain interval and nonlinear elsewhere?

**Tip:** If you have a table of values, always check the consistency of the slope to determine if the function is linear!

Determine whether the table represents a linear or nonlinear function.

$x$
5
7
9
11

$y$
-9
-3
-1
3

Learn how to determine if a table of values represents a linear or nonlinear function by checking the rate of change between points. This problem involves calculating slopes between points such as (5, -9) and (7, -3). Discover key concepts like rate of change and slopes, suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation