Holt McDougal Pre-Algebra Key Terms 8.1-8.5

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Questions and Answers

What is a relation?

A pairing of numbers in the domain with numbers in the range.

What is the range of a relation?

The output (y).

What is the domain in a relation?

The input (x).

What defines a function?

A relation when each input has exactly one output. Signup and view all the answers

What is the Vertical Line Test?

Using a graph and a vertical line to determine whether a relation is a function. Signup and view all the answers

What does an equation in two variables look like?

Example: 2x - y = 5. Signup and view all the answers

What is a solution to the equation in two variables?

An ordered pair (x,y) that produces a true statement when substituted into the equation. Signup and view all the answers

What is the graph of an equation of two variables?

The set of points on a coordinate plane that represent all possible solutions of the equation. Signup and view all the answers

What is a linear equation?

An equation whose graph is a line. Signup and view all the answers

What characterizes a linear function?

A function whose graph is a non-vertical line. Signup and view all the answers

What does function form mean?

The equation of a linear function is solved for y. Signup and view all the answers

What is the x-intercept?

The x coordinate of a point where a graph crosses the x-axis. Signup and view all the answers

What is the y-intercept?

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

What is slope?

The ratio of the line's vertical change to its horizontal change. Signup and view all the answers

What does rise refer to in slope?

A line's vertical change. Signup and view all the answers

What does run refer to in slope?

A line's horizontal change. Signup and view all the answers

Positive slope means the line rises.

True Signup and view all the answers

Negative slope means the line falls.

True Signup and view all the answers

Zero slope means the line is horizontal.

True Signup and view all the answers

Undefined slope means the line is horizontal.

False Signup and view all the answers

What is the Slope-Intercept Form?

A linear equation of the form y = mx + b; m is the slope, y-intercept is b. Signup and view all the answers

Study Notes

Key Terms in Relations and Functions

Relation: A pairing of values from the domain (input) with values from the range (output).
Range: Refers to the set of possible output values (y) from a function.
Domain: Represents the set of input values (x) for a function.
Function: A specific type of relation where each input corresponds to exactly one output.
Vertical Line Test: A graphical method to assess if a relation is a function by checking if any vertical line crosses the graph more than once.

Equations and Solutions

Equation in Two Variables: An example includes 2x - y = 5, representing a relationship between x and y.
Solution to the Equation in Two Variables: An ordered pair (x, y) that makes the equation true. For instance, (1, -3) satisfies 2(1) - (-3) = 5.
Graph of an Equation of Two Variables: The visual representation of all possible solutions on a coordinate plane.

Types of Equations

Linear Equation: An equation that graphically represents a straight line.
Linear Function: A specific type of function where the graph is a non-vertical line.

Function Form

Function Form: When a linear function equation is rearranged to isolate y. For instance, y = -3x + 7 is in function form, while 3x + y = 7 is not.

Intercepts and Slope

x-intercept: The point where the graph crosses the x-axis, denoting the x-coordinate at that intersection.
y-intercept: The point where the graph crosses the y-axis, indicating the y-coordinate at that intersection.
Slope: A measure of the steepness of a line calculated as the ratio of vertical change (rise) to horizontal change (run).

Slope Characteristics

Rise: Refers to the vertical change in the slope of a line.
Run: Refers to the horizontal change in the slope of a line.
Positive Slope: Occurs when the line rises as it moves from left to right.
Negative Slope: Arises when the line falls from left to right.
Zero Slope: Describes a horizontal line where there is no vertical change.
Undefined Slope: Characterizes a vertical line where horizontal change is zero.

Slope-Intercept Form

Slope-Intercept Form: The linear equation format y = mx + b, where m represents the slope and b denotes the y-intercept.

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Description

Test your understanding of key terms from Sections 8.1 to 8.5 of the Holt McDougal Larson Pre-Algebra textbook. This quiz covers essential vocabulary including relation, range, domain, function, and the vertical line test. Perfect for reinforcing your learning and preparing for assessments.