Proportional/Non-proportional Relationships Flashcards
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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?

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

    What is a linear relationship?

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

    What is the constant of proportionality?

    <p>The constant value of the ratio of two proportional quantities.</p> Signup and view all the answers

    What is a proportion?

    <p>An equation stating that two ratios are equal.</p> Signup and view all the answers

    What is a constant?

    <p>A value that does not change.</p> Signup and view all the answers

    What is slope?

    <p>The steepness of a line on a graph.</p> Signup and view all the answers

    What is the rate of change?

    <p>A ratio comparing the amount of change in a dependent variable to the independent variable.</p> Signup and view all the answers

    What does linear mean in mathematics?

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

    What is the origin in a coordinate plane?

    <p>The point where the x-axis and the y-axis intersect, (0,0).</p> Signup and view all the answers

    What is the y-intercept?

    <p>The y-coordinate of the point where a graph crosses the y-axis.</p> Signup and view all the answers

    What is the slope formula?

    <p>(y₂ - y₁) / (x₂ - x₁)</p> 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.

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    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.

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