Proportional/Non-proportional Relationships Flashcards

Questions and Answers

What is a proportional relationship?

A relationship with two quantities that have varying ratios

A relationship that can be represented by a quadratic equation

A relationship where the ratio is not constant

A relationship with a linear graph that goes through (0,0) (correct)

What defines a nonproportional relationship?

The graph is a straight line that does not pass through the origin.

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 is a linear relationship?

A relationship represented by a straight line in the form of y = mx + b. Signup and view all the answers

What is the constant of proportionality?

The constant value of the ratio of two proportional 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 slope?

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

What is the rate of change?

A ratio comparing the amount of change in a dependent variable to the 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 origin in a coordinate plane?

The point where the x-axis and the y-axis intersect, (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

What is the slope formula?

(y₂ - y₁) / (x₂ - x₁) Signup and view all the answers

Study Notes

Proportional Relationships

Defined as a relationship between two quantities where the ratio is constant.
Graphically represented as a straight line through the point (0,0).

Non-Proportional Relationships

Represented on a graph as a straight line that does not intersect the origin.

Rate

A mathematical expression comparing two quantities of different units.

Unit Rate

A special type of rate where the second quantity is one unit, often expressed as "per."

Linear Relationships

Always graph as straight lines and can be modeled by the equation y = mx + b, where m is the slope and b is the y-intercept.

Constant of Proportionality

The fixed ratio present in a proportional relationship, found by dividing y by x.

Proportion

An equation indicating that two ratios are equal, maintaining a balance between the quantities.

Constant

A value that remains unchanged in a given context.

Slope

Measures the steepness of a line and is calculated as the rise (change in y) over the run (change in x).

Rate of Change

Equivalent to slope, it compares changes in a dependent variable to those in an independent variable.

Linear Representation

A relationship or function that can be illustrated as a straight line on a graph.

Origin

The intersection point of the x-axis and y-axis on the coordinate plane, represented as (0,0).

y-Intercept

The y-coordinate of the point where a graph crosses the y-axis, crucial for understanding linear equations.

Slope Formula

Calculated as (y₂ - y₁) / (x₂ - x₁), used to find the slope between two points on a graph.

Description

Explore the concepts of proportional and non-proportional relationships with these informative flashcards. Each card defines key terms and illustrates the differences between the two types of relationships. Perfect for students learning about linear relationships in mathematics.