Graph Proportionality and the Origin

The video tutorial explains how to determine if a graph represents proportional quantities. It introduces the criteria for proportionality: the graph must be a straight line and pass through the origin (0,0). The tutorial provides examples to illustrate these concepts, showing graphs that meet or fail these criteria, and explains the reasoning behind each example.

What are the two criteria for determining if a graph shows a proportional relationship?

• The graph must be a curve and pass through the origin.

• The graph must be a line and pass through the origin.

• The graph must be a line and pass through any point.

• The graph must be a curve and pass through any point.

In the first example, why is the graph considered proportional?

• It forms a curve but does not pass through the origin.

• It forms a line and passes through the origin.

• It forms a curve and passes through the origin.

• It forms a line but does not pass through the origin.

What is the significance of the origin in determining proportionality?

• The graph must avoid any point to be proportional.

• The graph must avoid the origin to be proportional.

• The graph must pass through the origin to be proportional.

• The graph must pass through any point to be proportional.

In the second example, what is the reason the graph is not proportional?

• It forms a line and passes through the origin.

• It forms a curve and passes through the origin.

• It forms a curve but does not pass through the origin.

• It forms a line but does not pass through the origin.

What happens if a graph forms a line but does not pass through the origin?

• It is considered proportional.

• It is not considered proportional.

• It is considered a curve.

• It is considered a straight line.

In the third example, why is the graph not proportional?

• It does not form a line but passes through the origin.

• It forms a line and passes through the origin.

• It forms a curve and passes through the origin.

• It forms a line but does not pass through the origin.

What is the impact of a graph not forming a line on its proportionality?

• It is considered a curve.

• It is considered a straight line.

• It is not considered proportional.

• It is still considered proportional.

Which of the following is true for a graph that passes through the origin but does not form a line?

• It is considered a curve.

• It is considered a straight line.

• It is not considered proportional.

• It is considered proportional.

What is the role of the origin in the context of graph proportionality?

• It is irrelevant to proportionality.

• It is crucial for determining proportionality.

• It is only important for lines.

• It is only important for curves.

If a graph is a line and passes through the origin, what can be concluded?

• The graph is not proportional.

• The graph is a curve.

• The graph is proportional.

• The graph is a straight line but not proportional.