Let's analyze the mathematical expressions provided one by one:
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\(25 = x^2 + y^2\)
- Type: This is a nonlinear equation because it represents a circle (specifically, a circle with radius 5 centered at the origin).
- Function: This is not a function because for some values of \(x\), there are two corresponding values of \(y\) (one positive and one negative).
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\((y + 7) = 3(x - 2)\)
- Type: This is a linear equation in the form of \(y = mx + b\). It can be rewritten as \(y = 3x - 6\).
- Function: This is a function because for every \(x\) value, there is exactly one \(y\) value.
Summary:
| Expression | Linear | Nonlinear | Function | Not a Function | |-------------------------------------|--------------|-----------|-----------|-----------------| | \(25 = x^2 + y^2\) | | Nonlinear | | Not a Function | | \((y + 7) = 3(x - 2)\) | Linear | | Function | |