QQuestionMathematics
QuestionMathematics
Which graph represents a function with direct variation?
### Which graph represents a function with direct variation?
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Answer
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Step 1:Let me solve this step by step:
Step 2:: Recall the definition of direct variation
- Its equation has the form $$y = kx$$, where $$k$$ is a constant (non-zero)
- A direct variation function is a linear function that passes through the origin (0,0) - The graph of a direct variation function is always a straight line that passes through the point (0,0)
Step 3:: Examine the key characteristics of direct variation graphs
- Must pass through the origin (0,0) - Straight line - Line goes through the point (0,0) - Slope represents the constant of variation
Step 4:: Analyze each graph
- Graph A: Passes through (0,0) ✓ Straight line ✓ - Graph B: Does NOT pass through (0,0) ✗ - Graph C: Curved line ✗ - Graph D: Does NOT pass through (0,0) ✗
Step 5:: Confirm the characteristics of Graph A
- Passes through origin (0,0) - Straight line - Slope is constant - Represents a direct variation function
Final Answer
Graph A represents a function with direct variation.
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