Questions and Answers
What is a proportional relationship?
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?
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What is a linear relationship?
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What is the constant of proportionality?
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What is a proportion?
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What is a constant?
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What is slope?
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What is the rate of change?
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What does linear mean in mathematics?
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What is the origin in a coordinate plane?
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What is the y-intercept?
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What is the slope formula?
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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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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.