Linear Functions and Relationships

The video tutorial introduces Module 4, focusing on non-proportional relationships. It contrasts these with proportional relationships from Module 3, emphasizing that while both are linear, non-proportional relationships do not have a constant of proportionality. The tutorial provides examples of non-proportional linear relationships using tables and equations, demonstrating how to identify linearity through a constant rate of change. It concludes with a real-world example of plant growth to illustrate these concepts.

What is the main focus of Module 4 in the lesson?

• Quadratic equations

• Non-proportional relationships

• Graphing techniques

• Proportional relationships

In a non-proportional relationship, what remains constant?

• The product of x and y

• The sum of x and y

• The rate of change

• The ratio of y to x

How do you determine if a table represents a non-proportional linear relationship?

• By checking if the graph passes through the origin

• By ensuring the ratio of y to x is constant

• By calculating the sum of all x values

• By verifying the rate of change is constant

In the first example, what is the rate of change for the table provided?

• 3

• 2

• 4

• 1.5

What is the slope or rate of change in the second example?

• -2/3

• -1/3

• 1/3

• 2/3

When filling a table using an equation, what type of x-values should you choose?

• Negative numbers only

• Random numbers

• Large positive numbers

• Values that make sense in context

In the equation y = 3x - 1, what is the y-value when x is 0?

• 3

• 1

• 0

• -1

For the equation y = 1/2x + 3, what is the y-value when x is 4?

• 7

• 4

• 5

• 6

Why is it important to choose appropriate x-values in real-world problems?

• To make calculations easier

• To avoid negative results

• To ensure the graph passes through the origin

• To reflect realistic scenarios

In the plant growth example, what is the height of the plant after 3 days?

• 9 cm

• 12 cm

• 10 cm

• 11 cm