‘Which graph represents a function with direct variation
The Correct Answer and Explanation is:
✅ Correct Answer:
A graph that is a straight line passing through the origin (0, 0) represents a function with direct variation.
📘 Explanation
A direct variation is a type of linear relationship between two variables where one variable is a constant multiple of the other. It can be expressed by the equation:y=kxy = kxy=kx
Here, kkk is the constant of variation or slope, and it represents how much yyy changes for each unit change in xxx. This equation has no y-intercept other than 0, meaning the graph must pass through the origin (0, 0).
This is different from general linear equations like:y=mx+by = mx + by=mx+b
where b≠0b \neq 0b=0 would cause the line not to pass through the origin. Such lines do not represent direct variation.
Key Features of a Direct Variation Graph:
- Straight Line – The graph must be linear (not curved or broken).
- Passes Through Origin – The point (0, 0) must be on the line.
- Slope is Constant – The ratio yx\frac{y}{x}xy is the same for all points.
⚠️ What to Watch Out For:
- If a line is straight but does not pass through the origin, it is not a direct variation.
- Curved lines (like parabolas or circles) never represent direct variation.
- If the line has a break, gap, or undefined parts (like a vertical line), it is not a function.
✅ Summary:
To identify the graph of a function with direct variation:
- Look for a straight line.
- Confirm that it goes through (0, 0).
If both conditions are true, the graph does represent a direct variation.
