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

Tags

CCSS.7.RP.A.2D

Which of the following equations represents a direct variation?

• y = x^2 + 2x

• y = 2x + 3

• y = 3x - 1

• y = 4x

Tags

CCSS.7.RP.A.2B

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

• -6

• 6

• -3

• 0

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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

Tags

CCSS.7.RP.A.2A

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

• (0, 1)

• (0, -1)

• (1, 0)

• (-1, 0)

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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

• 3

• 0

• 5

• 8

Tags

CCSS.8.EE.B.5

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

• Neither

• Non-proportional

• Proportional

• Both

Tags

CCSS.7.RP.A.2A

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

• 2

• 10

• 3

• 5

Tags

CCSS.HSF.BF.A.2

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

• Both

• Neither

• Non-proportional

• Proportional

Tags

CCSS.7.RP.A.2D