direct and inverse variation

which graph represents a direct variation?

Question

direct and inverse variation

which graph represents a direct variation?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Direct Variation" ], "new_concepts": [], "current_concepts": [ "Direct Variation", "Inverse Variation" ] } ## Identify direct variation graph properties $$ y = kx \implies (0,0) \text{ is on the line} $$ ## Evaluate the given graphs $$ \begin{aligned} &\text{Graph 1 (top-left): Passes through } (0,0) \text{ and is a straight line.} \ &\text{Graph 2 (top-middle): Represents an inverse variation curve } y = \frac{k}{x}. \ &\text{Graph 3 (top-right): A straight line, but does not pass through } (0,0). \ &\text{Graph 4 (bottom-left): A curved line, not a straight line.} \end{aligned} $$ ## Select the correct option $$ \text{The first graph (top-left) represents direct variation.} $$

(A) The first graph (top-left) showing a straight line passing through the origin $(0,0)$

(B) The second graph (top-middle) showing a hyperbola

(C) The third graph (top-right) showing a line that does not pass through the origin

(D) The fourth graph (bottom-left) showing a curve

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Direct Variation" ] }

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Question

Explanation:

Identify direct variation graph properties

Evaluate the given graphs

Select the correct option

Answer: