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

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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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