https://file.aiquickdraw.com/mathbot/file/1729091372873jn1285u1.jpg

In the image, you are asked to identify which equation represents a **linear function**.

The equations provided are:

1. \( y = -3x^2 + 2 \)
2. \( y = -4x + 5 \)
3. \( y = x^3 \)
4. \( y = 2x^2 \)

A **linear function** has the form \( y = mx + b \), where \( m \) and \( b \) are constants, and \( x \) is raised only to the power of 1 (no squares or cubes of \( x \)).

- **Option 1**: \( y = -3x^2 + 2 \) is a quadratic function because \( x^2 \) is present.
- **Option 2**: \( y = -4x + 5 \) is a linear function because the highest power of \( x \) is 1.
- **Option 3**: \( y = x^3 \) is a cubic function due to the \( x^3 \) term.
- **Option 4**: \( y = 2x^2 \) is another quadratic function because of the \( x^2 \) term.

The correct answer is **Option 2: \( y = -4x + 5 \)**.

Would you like further clarification on this, or have any additional questions?

Here are 5 related questions to think about:
1. What is the general form of a quadratic function?
2. How do we identify a cubic function based on its equation?
3. What is the slope-intercept form of a linear equation?
4. How can you graph a linear function like \( y = -4x + 5 \)?
5. How do you determine if a function is non-linear by looking at its graph?

**Tip:** Always check the highest exponent of \( x \) in an equation to determine the type of function you're dealing with (linear, quadratic, cubic, etc.).

Which equation represents a linear function?

Learn how to identify which equation represents a linear function from multiple options. Understand the key difference between linear, quadratic, and cubic functions. This problem is suitable for students in Grades 7-9.

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