Identifying Proportional Relationships through Graphs

The video tutorial explores three different relationships between X and Y to determine if they are proportional. It explains that a proportional relationship has a constant ratio between Y and X, and its graph is a line through the origin. The first relationship is proportional with a constant ratio of 1/2. The second relationship is linear but not proportional as it doesn't pass through the origin. The third relationship is non-linear, resembling a quadratic function, and is also not proportional.

What is a key characteristic of a proportional relationship?

• The ratio between the two variables is always constant.

• The variables are always different.

• The ratio between the two variables is always changing.

• The variables are always equal.

In the first relationship, what is the constant ratio between Y and X?

• 1/2

• 4

• 1/4

• 2

What is the equation of the first relationship?

• Y = 2X

• Y = X + 1

• Y = 1/2X

• Y = X^2

Why is the first relationship considered proportional?

• It is a line that does not go through the origin.

• It is a line that goes through the origin.

• It has a changing ratio.

• It is not a line.

What is the ratio of Y to X for the second relationship when X is 2 and Y is 5?

• 5/2

• 1

• 2

• 3

Why is the second relationship not considered proportional?

• It has a constant ratio.

• The ratio between Y and X is not constant.

• It goes through the origin.

• It is not a line.

What is the equation that the second relationship could be sampled from?

• Y = 2X + 1

• Y = X + 2

• Y = 1/2X

• Y = X^2

What is the ratio of Y to X for the third relationship when X is 2 and Y is 4?

• 1

• 2

• 3

• 4

Why is the third relationship not considered proportional?

• It is a line that does not go through the origin.

• It is a line that goes through the origin.

• It is not a line.

• It has a constant ratio.

Which relationship is proportional?

• None of the relationships

• The third relationship

• The second relationship

• The first relationship