Exploring Proportional and Non-Proportional Relationships

This video tutorial for eighth-grade students covers the concepts of proportional and non-proportional relationships. It begins with an introduction to these concepts, followed by detailed explanations on how to identify proportional and non-proportional graphs and tables. Proportional graphs pass through the origin, while non-proportional graphs do not. For tables, proportionality is determined by consistent Y/X ratios, whereas non-proportional tables have varying ratios. The video concludes with instructions for the next assignments.

What is the main focus of the lesson?

• Understanding linear equations

• Learning about proportional and non-proportional relationships

• Studying quadratic functions

• Exploring geometric shapes

What is a key characteristic of a proportional graph?

• It crosses the y-axis at any point

• It crosses the x-axis at any point

• It passes through the origin

• It has a curved line

Which of the following is true for a proportional graph with a negative slope?

• It does not pass through the origin

• It passes through the origin

• It has a positive slope

• It crosses the y-axis at a non-zero point

What is the defining feature of a non-proportional graph?

• It does not pass through the origin

• It has a constant slope

• It has a positive slope

• It passes through the origin

In a non-proportional graph, what can the value of B be?

• Always negative

• Zero

• Any number except zero

• Always positive

How do you determine if a table is proportional?

• By checking if the values of X are all negative

• By checking if the values of Y are all positive

• By checking if X over Y is the same for all pairs

• By checking if Y over X is the same for all pairs

What is the slope if Y over X is the same for all pairs in a table?

• The sum of all X values

• The constant value obtained from Y over X

• The difference between the highest and lowest Y values

• The sum of all Y values

What indicates that a table is non-proportional?

• Y over X is the same for all pairs

• All X values are negative

• All Y values are positive

• Y over X is different for different pairs

If Y over X gives different results for different pairs, what does it mean?

• The table is proportional

• The table is non-proportional

• The values are incorrect

• The table needs more data

What should you do if you are unsure about the calculations in a table?

• Skip the question

• Use a calculator

• Guess the values

• Ask a friend