Understanding Proportional Relationships

Mr. Weaver introduces graphs of proportional relationships, explaining that they form a straight line through the origin. He uses examples like hamburger prices, trampoline park costs, and concert tickets to illustrate proportional and non-proportional relationships. The lesson emphasizes that for a graph to be proportional, it must be a straight line passing through the origin.

What is a key characteristic of a graph that represents a proportional relationship?

• It passes through the point (0,0).

• It does not intersect the axes.

• It forms a curved line.

• It has varying slopes.

In the hamburger cost example, what is the constant of proportionality?

• 3

• 2

• 5

• 4

In the hamburger example, what does the point (2,8) represent?

• 2 pounds of hamburger costing $8

• 8 pounds of hamburger costing $2

• 2 pounds of hamburger costing $4

• 8 pounds of hamburger costing $16

Why is the trampoline park example not a proportional relationship?

• The graph does not pass through the origin.

• The graph forms a straight line.

• The constants of proportionality are inconsistent.

• The graph has a constant slope.

What happens to the graph if the constant of proportionality changes?

• The graph becomes a curve.

• The graph remains a straight line.

• The graph shifts horizontally.

• The graph shifts vertically.

In the concert tickets example, why is the relationship not proportional?

• The parking fee is variable.

• The line does not pass through the origin.

• The cost per ticket is constant.

• The line is not straight.

In the concert tickets example, what is the initial cost before buying any tickets?

• $0

• $5

• $10

• $15

What is the significance of the point (0,0) in a proportional graph?

• It suggests the graph is incomplete.

• It shows the graph has a variable slope.

• It indicates the graph is non-linear.

• It confirms the graph is proportional.

Why might you choose not to connect points on a graph?

• The points form a straight line.

• The points represent discrete data.

• The points are too close together.

• The points are too far apart.

What is a common feature of non-proportional graphs?

• They do not form a straight line.

• They have a constant slope.

• They have varying constants of proportionality.

• They always pass through the origin.