https://file.aiquickdraw.com/mathbot/file/1726607166064e8d6b5ba.jpg

To determine if the function shown in the table is linear or nonlinear, we need to check the relationship between the values of \( x \) and \( y \). Specifically, in a linear function, the rate of change (or slope) between successive points should remain constant.

We can calculate the slope between pairs of points using the formula for slope:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's compute the slope for the pairs of points given in the table:

1. Between \( (9, 6) \) and \( (10, 14) \):
\[
\text{slope} = \frac{14 - 6}{10 - 9} = \frac{8}{1} = 8
\]

2. Between \( (10, 14) \) and \( (11, 20) \):
\[
\text{slope} = \frac{20 - 14}{11 - 10} = \frac{6}{1} = 6
\]

Since the slopes are different (8 and 6), the rate of change is not constant. Therefore, the function is **nonlinear**.

Would you like more details on this? Here are five related questions that might deepen your understanding:

1. What is the graphical representation of a linear function versus a nonlinear function?
2. How can you tell if a function is nonlinear by looking at an equation?
3. What other methods can be used to determine if a function is linear or nonlinear?
4. Can a function be nonlinear even if some of its points seem to follow a linear pattern?
5. How do systems of nonlinear equations differ from linear systems?

**Tip

The table shows a function. Is the function linear or nonlinear?

Learn how to determine whether a function is linear or nonlinear by calculating the rate of change using the slope formula. This example covers the points (9,6), (10,14), and (11,20) and shows how to check if the rate of change is constant. Suitable for students in 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