which equation represents a nonlinear function?

$x(y - 5) = 2$
$y - 2(x + 9) = 0$
$3y + 6(2 - x) = 5$
$2(y + x) = 0$

Question

which equation represents a nonlinear function?

$x(y - 5) = 2$
$y - 2(x + 9) = 0$
$3y + 6(2 - x) = 5$
$2(y + x) = 0$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Linear and Nonlinear Equations", "Identifying Nonlinear Functions" ], "current_concepts": [ "Linear and Nonlinear Equations", "Identifying Nonlinear Functions" ] } ## Define linear and nonlinear equations $$ \text{A linear equation in two variables can be written in the form } Ax + By = C. $$ ## Analyze each given equation $$ \begin{aligned} &\text{Option 1: } x(y - 5) = 2 \implies xy - 5x = 2 \quad (\text{Nonlinear due to the } xy \text{ term}) \ &\text{Option 2: } y - 2(x + 9) = 0 \implies y - 2x - 18 = 0 \implies -2x + y = 18 \quad (\text{Linear}) \ &\text{Option 3: } 3y + 6(2 - x) = 5 \implies 3y + 12 - 6x = 5 \implies -6x + 3y = -7 \quad (\text{Linear}) \ &\text{Option 4: } 2(y + x) = 0 \implies 2x + 2y = 0 \quad (\text{Linear}) \end{aligned} $$ ## Identify the nonlinear function $$ x(y - 5) = 2 $$

(A) $x(y-5) = 2$

(B) $y-2(x+9) = 0$

(C) $3y+6(2-x) = 5$

(D) $2(y+x) = 0$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear and Nonlinear Equations" ] }

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Explanation:

Define linear and nonlinear equations

Analyze each given equation

Identify the nonlinear function

Answer: