To determine which equation is linear, let’s analyze the options given in the image:

Definitions:

• A linear equation is an equation of the form $ax + by = c$, where $a$, $b$, and $c$ are constants. Both $x$ and $y$ must have a degree of 1, meaning there are no squares, products, or divisions of variables.

Analyzing each option:

1. $x^2 + y = 4$:

   • The $x^2$ term makes this a quadratic equation, not linear.

2. $x + y = 4$:

   • Both $x$ and $y$ have a degree of 1, and the equation is in standard linear form. This is a linear equation.

3. $xy = 4$:

   • The product $xy$ introduces non-linearity, so this is not a linear equation.

4. $\frac{1}{x} + y = 4$:

   • The $\frac{1}{x}$ term introduces a non-linear component (it behaves like $x^{-1}$), so this is not a linear equation.

Final Answer:

The correct choice is $b. x + y = 4$.

Do you want a detailed explanation of why the other equations fail to be linear?

Here are five related questions to deepen your understanding:

1. What are the characteristics of a linear equation in three variables?
2. Can a linear equation contain absolute value terms? Why or why not?
3. What is the geometric interpretation of a linear equation in two variables?
4. How do linear equations differ from quadratic equations?
5. Can linear equations have coefficients that are fractions or decimals?

Tip: Always check the powers and products of the variables in an equation to classify its type!