1. The problem asks to classify each equation as linear or nonlinear. 2. A linear equation in two variables $x$ and $y$ has the form $$Ax + By = C$$ where $A$, $B$, and $C$ are constants, and the variables are only to the first power. 3. Let's analyze each equation: - Equation 1: $3x + 2y = 26$ - Both $x$ and $y$ are to the first power. - This fits the linear form. - Equation 2: $y = 3x^3 + 4$ - The term $x^3$ has $x$ raised to the third power. - This is nonlinear. - Equation 3: $y = 5$ - This is a constant function, which is linear. - Equation 4: $5y - 8x^2 = -10$ - The term $x^2$ has $x$ squared. - This is nonlinear. 4. Final classification: - $3x + 2y = 26$: Linear Function - $y = 3x^3 + 4$: Nonlinear Function - $y = 5$: Linear Function - $5y - 8x^2 = -10$: Nonlinear Function