Proportional and Linear Relationships Quiz

Podcast Beta

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is a proportional relationship?

A relationship where the ratio of one quantity to the other is constant (correct)

A relationship that is represented by a straight line on a graph

A relationship that can be expressed in the form y = mx + b

A relationship that does not pass through the origin

What defines a non-proportional relationship?

The line passes through the origin

The relationship is proportional

There is a constant rate of change

It can be expressed as y = mx + b where b is not 0 (correct)

What is a rate?

A ratio of two quantities measured in different units.

What is a unit rate?

A rate in which the second quantity is one unit. Signup and view all the answers

What does a linear relationship represent?

A change in the independent variable causes a proportionally equal change in the dependent variable. Signup and view all the answers

What is the constant of proportionality?

In a proportional relationship, it is the constant value of the ratio of two quantities. Signup and view all the answers

What is a proportion?

An equation stating that two ratios are equal. Signup and view all the answers

What is a constant?

A value that does not change. Signup and view all the answers

What is direct variation?

Increase in one variable causes a proportional increase in another variable. Signup and view all the answers

What is the slope?

The steepness of a line on a graph. Signup and view all the answers

What does 'change in y values' refer to?

The difference in the change of the y values in a table (y2 - y1). Signup and view all the answers

What does 'change in x values' refer to?

The difference in the change of the x values in a table (x2 - x1). Signup and view all the answers

What is the rate of change?

A ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable. Signup and view all the answers

What does linear mean in mathematics?

A relationship or function that can be represented by a straight line. Signup and view all the answers

What is the delta symbol for change?

Δ Signup and view all the answers

What does Δy / Δx represent?

Change in the y values divided by the change in the x values. Signup and view all the answers

What is the origin in a coordinate plane?

(0,0) Signup and view all the answers

What is the y-intercept?

The y coordinate of the point where a graph crosses the y axis. Signup and view all the answers

Study Notes

Proportional Relationships

Defined as a relationship where the ratio between two quantities remains constant.
Typically represented by the equation ( y = kx ), where ( k ) is the constant of proportionality.

Non-Proportional Relationships

Expressed in the form ( y = mx + b ) with ( b \neq 0 ).
The graph is a straight line that does not intersect the origin.

Rate and Unit Rate

A rate compares two quantities with different units.
A unit rate compares to one unit of the second quantity, often expressed as "per".

Linear Relationships

Changes in the independent variable ( x ) result in equal proportional changes in the dependent variable ( y ).
Always represented by straight line graphs in the form ( y = mx + b ).

Constant of Proportionality

The fixed ratio in a proportional relationship typically written as ( y = kx ).

Proportion

An equation indicating that two ratios are equivalent.

Constants

Values that remain unchanged in the context of a relationship.

Direct Variation

Describes how an increase or decrease in one variable proportionally affects another variable, shown as ( y = kx ).

Slope

Represents the steepness of a line on a graph, calculated as the ratio of the change in ( y ) values to the change in ( x ) values (( \text{slope} = \frac{\Delta y}{\Delta x} )).

Change in Values

Change in ( y ) values is calculated as ( y_2 - y_1 ).
Change in ( x ) values is calculated as ( x_2 - x_1 ).

Rate of Change

The ratio comparing the change in a dependent variable to the change in an independent variable, synonymous with slope.

Linear Function

A linear relationship or function can be depicted by a straight line on a graph.

Delta Symbol (Δ)

Represents change or difference, simplifying the description of variations in values.

Coordinate System

The origin is the point where the x-axis and y-axis meet, located at (0,0).

Y-Intercept

The coordinate that represents where a graph intersects the y-axis.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your knowledge on proportional and linear relationships with this quiz. Explore concepts such as the constant of proportionality, rates, and the differences between proportional and non-proportional relationships. Get ready to dive into the world of equations and graphs!