Holt McDougal Pre-Algebra Key Terms 8.1-8.5

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.