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# Course 3 Chapter 3 Vocabulary

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@AmicableNeodymium

### What is the constant of proportionality?

The constant ratio in a proportional linear relationship

### What is the constant of variation?

A constant ratio in a direct variation

### What does constant rate of change refer to?

The rate of change between any two points in a linear relationship is the same or constant

### What is a direct variation?

<p>A relationship between two variable quantities with a constant ratio</p> Signup and view all the answers

### What characterizes a linear relationship?

<p>A relationship that has a straight line graph</p> Signup and view all the answers

### What is the point-slope form of an equation?

<p>An equation of the form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a given point on a nonvertical line</p> Signup and view all the answers

### What does rise refer to in the context of a line?

<p>The vertical change between any two points on a line</p> Signup and view all the answers

### What does run refer to in the context of a line?

<p>The horizontal change between any two points on a line</p> Signup and view all the answers

### What is slope in the context of a line?

<p>The rate of change between any two points on a line, the ratio of the rise to the run</p> Signup and view all the answers

### What is the slope-intercept form of an equation?

<p>An equation written in the form y = mx + b, where m is the slope and b is the Y-intercept</p> Signup and view all the answers

### What is the standard form of an equation?

<p>An equation written in the form Ax + By = C</p> Signup and view all the answers

### What is substitution in algebra?

<p>An algebraic model that can be used to find the exact solution of a system of equations</p> Signup and view all the answers

### What is a system of equations?

<p>A set of two or more equations with the same variables</p> Signup and view all the answers

### What is the x-intercept?

<p>The x-coordinate of the point where the line crosses the x-axis</p> Signup and view all the answers

### What is the y-intercept?

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

## Study Notes

### Key Vocabulary Terms

• Constant of proportionality

• Represents a specific ratio in a proportional linear relationship.
• Constant of variation

• Indicates a constant ratio in a direct variation scenario.
• Constant rate of change

• Refers to a uniform rate of change between any two points on a linear graph, maintaining consistency.
• Direct variation

• Describes a relationship between two variable quantities characterized by a constant ratio; as one variable changes, the other does in a proportional manner.
• Linear relationship

• A relationship depicted by a straight line when graphed, illustrating a consistent change between variables.

### Equations and Forms

• Point slope form

• Structured as y - y1 = m(x - x1), where m signifies the slope and (x1, y1) denotes a specific point on a nonvertical line.
• Slope

• Represents the rate of change between points on a line; calculated as the ratio of vertical change (rise) to horizontal change (run).
• Slope-intercept form

• Expressed as y = mx + b; here, m stands for the slope and b indicates the y-intercept of the line.
• Standard form

• Formulated as Ax + By = c, where A, B, and C are constants, and x and y are variables.

### Changes in the Graph

• Rise

• The vertical change observed between two points on a line.
• Run

• The horizontal change measured between two points on a line.
• X-intercept

• The x-coordinate where the line intersects the x-axis, reflecting the point at which y equals zero.
• Y-intercept

• The y-coordinate where the line crosses the y-axis, indicating the point at which x equals zero.

### Systems and Solutions

• Substitution

• An algebraic method used to find exact solutions of a system of equations by replacing a variable with an equivalent expression.
• System of equations

• Consists of two or more equations sharing the same variables, which can be solved simultaneously to find common solutions.

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## Description

Test your knowledge of key vocabulary related to equations in two variables with this flashcard quiz. Each term is defined clearly, helping you understand concepts such as direct variation and constant rates of change. Ideal for students mastering algebra concepts.

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