Exploring Proportional and Nonproportional Relationships

The video tutorial discusses linear functions, focusing on proportional and non-proportional relationships. It explains the concept of a constant rate of change and how it relates to linear equations. The tutorial covers how to identify proportional relationships using the equation y=kx and graphing techniques. It also explores non-proportional relationships, emphasizing the importance of the rate of change and how to derive equations for these relationships.

What is a key characteristic of linear functions?

• They have no rate of change.

• They always curve.

• They have a constant rate of change.

• They have a variable rate of change.

In a proportional relationship, what form does the equation take?

• y = k/x

• y = mx + b

• y = kx

• y = x^2

What is the value of k in the equation y = kx if the relationship is proportional?

• k must be negative.

• k cannot be zero.

• k must be zero.

• k can be zero.

When graphing data, what indicates a linear relationship?

• The points form a curve.

• The points form a straight line.

• The points are scattered randomly.

• The points form a zigzag pattern.

What is the constant rate of change in the given table where 1 hour corresponds to 50 miles?

• 100

• 50

• 75

• 25

How do you verify the correctness of an equation representing a linear relationship?

• By ensuring it has a variable rate of change.

• By testing it with the given data points.

• By comparing it with a different equation.

• By checking if it passes through the origin.

What is the predicted number of miles driven in 8 hours using the equation y = 50h?

• 450 miles

• 300 miles

• 350 miles

• 400 miles

What makes a relationship non-proportional?

• It has a constant rate of change.

• It passes through the origin.

• It does not pass through the origin.

• It forms a straight line.

What is the rate of change if the y-values increase by 3 for every 1 increase in x?

• 4

• 2

• 3

• 1

What is the correct equation for a non-proportional relationship where the rate of change is 3 and the y-values are 2 more than the expected output?

• y = 3x + 2

• y = 3x - 2

• y = 2x + 3

• y = 2x - 3