Understanding Proportional and Non-Proportional Relationships

This video tutorial covers the concepts of proportional and non-proportional situations, focusing on how to distinguish between them using graphs, equations, and tables. It explains that a linear relationship is proportional if it passes through the origin, otherwise it is non-proportional. The tutorial also provides practical examples, such as sales tax and cost comparisons, to illustrate these concepts in real-world scenarios.

What is a key characteristic of a non-linear relationship?

• It has a constant slope.

• It graphs a curve.

• It always goes through the origin.

• It graphs a straight line.

When is a linear relationship considered proportional?

• When it forms a curve.

• When it has a y-intercept other than zero.

• When it has a positive slope.

• When it passes through the origin.

Which equation represents a proportional relationship?

• y = 4x

• y = 2x - 7

• y = 5x + 10

• y = 3x + 5

How can you determine if a table represents a proportional relationship?

• By ensuring the difference between x and y is constant.

• By checking if the product of x and y is constant.

• By verifying if the ratio of y to x is constant.

• By checking if the sum of x and y is constant.

In a table, if the ratio of y to x is not constant, what does it indicate?

• The relationship is non-proportional.

• The relationship is proportional.

• The relationship is linear.

• The relationship is non-linear.

What is the hourly rate for Arena A in the laser tag example?

• $200 per hour

• $225 per hour

• $250 per hour

• $275 per hour

Which arena has an initial fee in the laser tag example?

• Both Arena A and B

• Neither Arena A nor B

• Arena B

• Arena A

In the painter example, what is the hourly rate for Painter A?

• $65 per hour

• $35 per hour

• $45 per hour

• $55 per hour

What makes Painter B's charges non-proportional?

• The hourly rate is constant.

• The initial fee is zero.

• The ratio of y to x is not constant.

• The charges are based on a fixed rate.

In the test prep example, which center is cheaper for more than 20 hours?

• Test Prep A

• Test Prep B

• Both are the same

• Neither is cheaper