Proportional and Non-Proportional Relationships

This lesson introduces graphs of proportional relationships, using the example of buying blueberries at a constant rate of six dollars per pound. It explains how to calculate costs using the constant of proportionality and how to graph these relationships. The lesson also covers non-proportional examples, such as buying sandwiches, and provides criteria for identifying proportional relationships in graphs.

What is the constant of proportionality when buying blueberries at $6 per pound?

• $5 per pound

• $6 per pound

• $7 per pound

• $8 per pound

If you buy 3 pounds of blueberries, how much will it cost?

• $12

• $15

• $18

• $21

Which equation represents the cost of blueberries in terms of weight?

• y = 8x

• y = 6x

• y = 5x

• y = 7x

Why might you not connect points on a graph when representing the sale of sandwiches?

• Because sandwiches are sold in dozens

• Because sandwiches are always sold in pairs

• Because sandwiches are not sold in fractional amounts

• Because sandwiches are sold by weight

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

• It is a straight line that does not pass through the origin

• It is a dotted line

• It is a straight line that passes through the origin

• It is a curve

If a graph is a curve, what does it indicate about the relationship?

• It is a proportional relationship

• It is not a proportional relationship

• It is a quadratic relationship

• It is a linear relationship

What happens to y when x is doubled in a proportional relationship?

• y remains the same

• y is tripled

• y is halved

• y is doubled

In a non-proportional relationship, if x doubles from 2 to 4, what happens to y?

• y decreases

• y remains the same

• y doubles

• y increases but does not double

Which of the following is NOT a characteristic of a proportional relationship graph?

• It passes through the origin

• It is a curve

• It is a straight line

• It has a constant slope

If a graph does not pass through the origin, what does it indicate about the relationship?

• It is a linear relationship

• It is a proportional relationship

• It is not a proportional relationship

• It is a quadratic relationship