Glencoe Algebra 1 Chapter 3 Vocabulary

Questions and Answers

What is the definition of a Linear Equation?

An equation that has no solutions

An equation that forms a circle when graphed

An equation that forms a line when graphed (correct)

An equation that only contains one variable

What is the Standard Form of a linear equation?

Ax + By = C

What is a Constant in algebra?

A monomial that is a real number

What is an X-Intercept?

The x-coordinate of the point at which the graph crosses the x-axis Signup and view all the answers

What is a Y-Intercept?

The y-coordinate of the point at which the graph crosses the y-axis Signup and view all the answers

What is a Linear Function?

A function when the graph is a line Signup and view all the answers

What is the Parent Function in linear equations?

f(x) = -x Signup and view all the answers

What is a Family of Graphs?

A group of graphs with one or more similar characteristics Signup and view all the answers

What is a Root of an equation?

The solution of an equation Signup and view all the answers

What is the Rate of Change?

A ratio that describes how much one quantity changes with respect to a change in another quantity Signup and view all the answers

What is Slope?

The change in x-coordinates over the change in y-coordinates (Horizontal/Vertical) Signup and view all the answers

What is Direct Variation?

The equation y = kx; where 'k' doesn't equal zero Signup and view all the answers

What is the Constant of Variation?

When y = kx illustrates a constant rate of change, then k is the constant of variation Signup and view all the answers

Study Notes

Linear Equations and Functions

Linear equation produces a line when graphed, typically structured as Ax + By = C.
Standard form representation of a linear equation is also Ax + By = C.
A linear function is marked by a graph that results in a line.

Key Concepts

Constants refer to monomials represented by a real number, remaining unchanged throughout equations.
X-intercept indicates where the graph intersects the x-axis, defined by its x-coordinate.
Y-intercept denotes the point where the graph crosses the y-axis, described by its y-coordinate.

Functions and Characteristics

The parent function, f(x) = -x, is the simplest form of a linear function.
A family of graphs consists of multiple graphs sharing similar features.

Solutions and Rates

The root of an equation signifies its solution or the value(s) that satisfy it.
Rate of change quantifies how one quantity alters concerning another, expressed as a ratio.

Slope and Variation

Slope is calculated as the change in y-coordinates divided by the change in x-coordinates, showcasing horizontal and vertical shifts.
Direct variation is defined by the equation y = kx, where k is a non-zero constant. This represents a proportional relationship between y and x.
The constant of variation (constant of proportionality) is the value k in the direct variation equation, indicating consistent rate changes.

Description

Test your knowledge of key vocabulary from Chapter 3 of Glencoe Algebra 1. This quiz features essential terms such as linear equations, standard form, and intercepts. Perfect for students looking to strengthen their understanding of algebra concepts.