A function is linear if it satisfies two main criteria:

1. **It can be written in the form** \( f(x) = mx + b \), where \( m \) and \( b \) are constants:
   - Here, \( m \) represents the slope, indicating the rate of change of the function, and \( b \) is the y-intercept, showing where the function crosses the y-axis.
   - This form ensures that the graph of the function is a straight line.

2. **It has a constant rate of change** (slope):
   - In a linear function, the difference in \( f(x) \) values for equal differences in \( x \) values remains constant.
   - This can be tested by calculating the slope between any two points on the function. If the slope remains the same for all pairs of points, the function is linear.

### Properties of Linear Functions
- The graph is always a straight line.
- The degree (highest power of \( x \)) in a linear equation is 1, meaning no exponents on \( x \) are greater than 1.
- Linear functions do not have curves, sharp turns, or bends in their graph.

Would you like to see a specific example of testing whether a function is linear?

#### Related Questions:
1. What distinguishes a linear function from a nonlinear one?
2. How do you calculate the slope of a linear function?
3. Can a linear function have more than one variable?
4. What is the role of the y-intercept in linear functions?
5. How does a linear function differ from an affine function?

#### Tip:
For any given function, if you see terms like \( x^2 \) or \( x/y \), the function is nonlinear.

Discover how to determine if a function is linear with a detailed explanation of the linear function formula and its properties. This guide covers algebraic concepts like slope, the y-intercept, and constant rate of change, suitable for students in Grades 8-10.

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