To determine which of the given equations is not a linear equation, we need to check if each equation can be written in the standard form of a linear equation. A linear equation involves variables (like \( x \) and \( y \)) raised only to the first power and does not include products of these variables or any non-linear functions like \(\sin(x)\) or \(\exp(y)\).
Let's examine each equation:
### Equation A: \(\frac{1}{2} x + 3 y = 2\)
Here, \(\frac{1}{2} x\) and \(3 y\) are both linear terms because each variable is raised to the power of 1. This is a standard form linear equation.
### Equation B: \(x^3 - 5 y^2 = 4\)
In this equation, \(x\) is raised to the power of 3 and \(y\) is raised to the power of 2. Both of these terms are non-linear because the variables \(x\) and \(y\) are not raised solely to the first power.
### Equation C: \(x = 2\)
This represents a vertical line, which is indeed a linear equation because it can be viewed as \(1 \cdot x + 0 \cdot y = 2\).
### Equation D: \(y = 4\)
Similarly, this represents a horizontal line, which is also a linear equation because it can be seen as \(0 \cdot x + 1 \cdot y = 4\).
From this analysis, we can clearly see that the equation which is not a linear equation is:
[tex]\[
B) x^3 - 5 y^2 = 4
\][/tex]
So, the answer is B.
