Exploring Proportional vs Nonproportional Relationships

This video tutorial covers the concepts of proportional and non-proportional relationships in linear equations. It begins with an introduction to proportional relationships, explaining direct variation and how to identify them through equations like y = kx. The tutorial provides examples to illustrate these concepts, followed by a discussion on non-proportional relationships, highlighting the impact of additional constants in equations. The video also includes exercises on completing tables and writing equations, graphing, and identifying relationships. Finally, it reviews arithmetic sequences and their connection to proportionality.

What is the form of the equation for a proportional relationship?

• y = kx

• y = kx + b

• y = ax^2 + bx + c

• y = mx + c

Which of the following equations represents a direct variation?

• y = x^2 + 2x

• y = 2x + 3

• y = 3x - 1

• y = 4x

If y = 3x, what is the y-value when x = -2?

• -6

• 6

• -3

• 0

What additional term in an equation makes a relationship non-proportional?

• A cubic term

• A squared term

• A variable term

• A constant term

Which of the following equations is non-proportional?

• y = 4x

• y = 2x - 1

• y = 3x

• y = 5x

What is the y-intercept of the equation y = 2x - 1?

• (0, 1)

• (0, -1)

• (1, 0)

• (-1, 0)

In the equation y = 5x + 3, what is the slope?

• 3

• 0

• 5

• 8

For the sequence 1, 3, 5, 7, is it proportional or non-proportional?

• Neither

• Non-proportional

• Proportional

• Both

What is the common difference in the arithmetic sequence 5, 10, 15, 20?

• 2

• 10

• 3

• 5

If the function for an arithmetic sequence is f(x) = 5x, is it proportional or non-proportional?

• Both

• Neither

• Non-proportional

• Proportional