Exploring Proportional and Non-Proportional Relationships

The video tutorial explains proportional relationships, focusing on graphs, equations, and tables. It highlights that proportional graphs are straight lines passing through the origin, while non-proportional graphs do not. Proportional equations are in the form y = kx, where k is the constant of proportionality, unlike non-proportional equations that include additional constants or powers. In tables, proportional relationships start at (0,0) and maintain equal y/x ratios, whereas non-proportional tables do not.

What is a key characteristic of a proportional graph?

• It has a curved line.

• It passes through the origin.

• It has a zigzag line.

• It does not pass through the origin.

In a proportional relationship, how do the quantities vary?

• One remains constant.

• At the same rate.

• One decreases while the other increases.

• At different rates.

Why is a graph with a straight line that does not pass through the origin considered non-proportional?

• Because it has a constant slope.

• Because it does not pass through the origin.

• Because it passes through the origin.

• Because it is not a straight line.

Which of the following is a characteristic of non-proportional graphs?

• They always pass through the origin.

• They have lines that do not pass through the origin or are not straight.

• They have straight lines that pass through the origin.

• They have equal ratios of y to x.

What form must a proportional equation take?

• y = kx^2

• y = kx - c

• y = kx

• y = kx + c

In a non-proportional equation, what additional elements might be present?

• Only multiplication by a constant.

• A constant added or subtracted, or a power.

• Only addition by a constant.

• Only division by a constant.

What is a key feature of proportional tables?

• They start with 0,3 and have different ratios of y to x.

• They start with 0,3 and have equal ratios of y to x.

• They start with 0,0 and have equal ratios of y to x.

• They start with 0,0 and have different ratios of y to x.

In a proportional table, what is true about the ratios of y to x?

• They are always zero.

• They are sometimes equal.

• They are all equal.

• They are all different.

What is a characteristic of non-proportional tables?

• They start with 0,0 and have equal ratios of y to x.

• They start with 0,0 and have different ratios of y to x.

• They do not start with 0,0 and have different ratios of y to x.

• They do not start with 0,0 and have equal ratios of y to x.

In a non-proportional table, what is true about the ratios of y to x?

• They are all equal.

• They are always zero.

• They are all different.

• They are sometimes equal.