Algebra Chapter 4 Check Flashcards

Questions and Answers

What is a linear function?

A function whose graph forms a straight line

What is a linear equation?

Any equation that can be written in the standard form Ax + By = C

What is an x-intercept?

The x-coordinate of the point where the graph intersects the x-axis

What is a y-intercept?

The y-coordinate of the point where the graph intersects the y-axis Signup and view all the answers

What is the rate of change?

A ratio that compares the amount of change in the dependent variable to the amount of change in an independent variable. Signup and view all the answers

What is rise in the context of a graph?

The difference in the y-values of 2 points on a line Signup and view all the answers

What is run in the context of a graph?

The difference in the x-values of 2 points on a line Signup and view all the answers

What is slope?

The ratio of rise to run for any two points on a line Signup and view all the answers

What is direct variation?

A special type of linear relationship that can be written in the form y = kx Signup and view all the answers

What is the constant of variation?

In the form y = kx, where k is a nonzero constant Signup and view all the answers

Study Notes

Linear Functions and Equations

A linear function presents a graph that forms a straight line, depicting a constant rate of change.
Linear equations can be expressed in the standard form (Ax + By = C), where A, B, and C are constants.

Intercepts

The x-intercept is where the graph meets the x-axis, characterized by a y-coordinate of 0.
The y-intercept occurs where the graph intersects the y-axis, noted by an x-coordinate of 0.

Change and Slope

The rate of change measures the variation in the dependent variable against the independent variable, providing insights into relationships between them.
Rise is defined as the difference in the y-values between two points on a line, indicating vertical change.
Run represents the difference in the x-values of two points on a line, reflecting horizontal change.
Slope is calculated as the ratio of rise to run, representing the steepness and direction of the line.

Variations

Direct variation occurs when there is a linear relationship expressed in the form (y = kx), indicating that y changes directly with x.
The constant of variation (k) in the equation (y = kx) is a nonzero constant that represents the proportional relationship between y and x.

Description

Test your knowledge of key concepts from Algebra Chapter 4 with these flashcards. You'll encounter definitions for linear functions, equations, and intercepts. Perfect for reinforcing your understanding of these fundamental topics.