Question

Rob says that this graph shows a proportional relationship. Is he correct? Explain.
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Answer 1

I can’t see the image file you attached. To answer whether the graph shows a proportional relationship I need either a description of the graph or a couple of points from it. Meanwhile, here is how you can decide and how to explain your answer:

Rules to check for a proportional relationship
- A proportional relationship between x and y has the form y = kx (k constant).
- On a graph this is a straight line that passes through the origin (0,0).
- Equivalently, any two nonzero points (x1,y1) and (x2,y2) on the graph must have the same ratio y1/x1 = y2/x2.

What to do with the graph
1. Does the line pass through the origin (0,0)?
- If yes → it could be proportional. Check one more point to confirm the ratio is constant.
- If no → it is not proportional.
2. Or pick two visible points (x1,y1) and (x2,y2) and compute y1/x1 and y2/x2. If the ratios are equal, it is proportional; if not, it isn’t.

Example explanations you can use
- If the line does not go through (0,0): “No. The line does not pass through the origin (the y-intercept is not 0), so y is not directly proportional to x.”
- If the line goes through (0,0) and ratios match: “Yes. The line goes through the origin and every point satisfies y = kx (for example y/x = k for two points), so it’s proportional.”

If you tell me two points from the graph or describe whether it passes through (0,0), I’ll give the exact yes/no answer and a short explanation.