Let's classify each equation as either defining \( y \) as a linear or nonlinear function of \( x \):
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\( y = 7 \times 4x \)
- Linear (can be simplified to \( y = 28x \))
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\( y = (2x + 5)^2 \)
- Nonlinear (it is a quadratic function)
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\( y = 10x^2 \)
- Nonlinear (it is a quadratic function)
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\( y = 5x - 3 \)
- Linear (it is a linear equation)
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\( y = 2x \)
- Linear (it is a linear equation)
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\( y = 2x^3 + 1 \)
- Nonlinear (it is a polynomial function of degree 3)
Here’s the classification:
| Equation | Linear/Nonlinear | |------------------------------|------------------| | \( y = 7 \times 4x \) | Linear | | \( y = (2x + 5)^2 \) | Nonlinear | | \( y = 10x^2 \) | Nonlinear | | \( y = 5x - 3 \) | Linear | | \( y = 2x \) | Linear | | \( y = 2x^3 + 1 \) | Nonlinear |