Algebra Class: Constants and Variations

Questions and Answers

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 is the Constant Rate of Change?

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

What is Direct Variation?

a relationship between two variable quantities with a constant ratio Signup and view all the answers

What are Linear Relationships?

a relationship that has a straight-line graph Signup and view all the answers

What is the Point-Slope Form?

an formula for finding the equation of a line when you know the slope and a point on the line Signup and view all the answers

What does 'Run' refer to in linear relationships?

the horizontal change between any two points on a line Signup and view all the answers

What is Slope?

the rate of change between any two points on a line; 'rise over run;' 'change in y over change in x' Signup and view all the answers

What is the Slope-Intercept Form?

an equation written in the form y=mx + b where m is slope and b is the y-intercept Signup and view all the answers

What is Standard Form?

an linear equation written so the variables are on one side of the equation and the constant is on the other Signup and view all the answers

What is Substitution in systems of equations?

an algebraic model that can be used to find the exact solution of a system of equations Signup and view all the answers

What are Systems of Equations?

a set of two or more equations with the same variable Signup and view all the answers

What is an x-Intercept?

where the line crosses the x-axis Signup and view all the answers

What is a y-Intercept?

where the line crosses the y-axis Signup and view all the answers

Study Notes

Constants and Variations

Constant of Proportionality: Specific constant ratio found in a proportional linear relationship, crucial for understanding direct relationships between variables.
Constant of Variation: Maintains a fixed ratio in direct variation scenarios, linking changes in one variable directly to changes in another.
Constant Rate of Change: In a linear relationship, the rate of change between any two points remains constant, facilitating predictions on linear graphs.

Relationships and Forms

Direct Variation: An established relationship between two variable quantities showcasing a constant ratio, essential in many mathematical problems.
Linear Relationships: Defined by a straight-line graph, these relationships illustrate how changes in one variable consistently affect another.

Key Mathematical Forms

Point-Slope Form: Useful for finding the equation of a line when the slope and a specific point on the line are known.
Slope-Intercept Form: Expressed as y = mx + b, where 'm' represents the slope and 'b' the y-intercept, this form is fundamental for graphing linear equations.
Standard Form: Written as an equation where all variables reside on one side and the constant on the other, useful for many algebraic manipulations.

Slope and Intercepts

Run: Refers to the horizontal change between two points on a line, which, when paired with the 'rise,' helps determine the slope.
Slope: The ratio of vertical change to horizontal change, interpreted as "rise over run," a central concept for understanding line steepness.
x-Intercept: The point at which a line crosses the x-axis, indicating where the output (y) is zero.
y-Intercept: The point where a line crosses the y-axis, showing where the input (x) is zero.

Equations and Systems

Substitution: An algebraic method utilized to solve systems of equations, enabling the determination of exact solutions for multiple equations.
Systems of Equations: A collection of two or more equations sharing the same variable, often analyzed together to find common solutions.

Description

Test your understanding of constants and variations in algebra. This quiz covers concepts such as the constant of proportionality, direct variation, and linear relationships. Get ready to explore the key mathematical forms that help define these relationships!