classify the relations below as either "linear" or "non-linear"
step by step
1. 2x+7y=14
2.x^2-6=y

### 1. \( 2x + 7y = 14 \)

- **Step 1**: This equation is in the form \( Ax + By = C \), where \( A \), \( B \), and \( C \) are constants.
- **Step 2**: There are no exponents or products of \( x \) and \( y \) beyond degree 1. The variables \( x \) and \( y \) are both raised to the power of 1.
- **Conclusion**: Since it fits the form of a linear equation (both \( x \) and \( y \) are raised to the first power and no terms like \( x^2 \), \( y^2 \), or \( xy \)), this equation is **linear**.

### 2. \( x^2 - 6 = y \)

- **Step 1**: The term \( x^2 \) involves an exponent of 2, which makes the relation between \( x \) and \( y \) quadratic.
- **Step 2**: Any equation that includes terms where the variable is raised to a power other than 1 (in this case, \( x^2 \)) is non-linear.
- **Conclusion**: Since this equation has \( x^2 \), it is a quadratic equation and is therefore **non-linear**.

### Summary:
1. \( 2x + 7y = 14 \) is **linear**.
2. \( x^2 - 6 = y \) is **non-linear**.

Do you want further details on any of these steps?

Here are 5 related questions for you:
1. What are the general forms of linear and non-linear equations?
2. How can you graph a linear equation?
3. How do quadratic equations differ from linear ones visually?
4. Can a system of equations be both linear and non-linear?
5. What are common applications of linear equations in real life?

**Tip**: Linear equations always graph as straight lines, while non-linear equations can form curves like parabolas, circles, or more complex shapes.

classify the relations below as either 'linear' or 'non-linear'
step by step
1. 2x+7y=14
2. x^2-6=y

Step-by-step classification of the equations 2x + 7y = 14 (linear) and x^2 - 6 = y (non-linear). Learn the difference between linear and quadratic equations and how to identify them. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation