Ch 3 - Proportional Relationships & Slope

Questions and Answers

What is a linear relationship?

A relationship that varies non-linearly

A relationship that has a curved graph

A relationship of three or more quantities

A relationship of two quantities that has a straight line graph (correct)

What is the constant rate of change in a linear relationship?

The rate of change between any two points is the same or constant.

Define unit rate.

A rate or ratio with a denominator of 1.

What does the slope represent?

The rate of change between any two points on a line. Signup and view all the answers

What does 'rise' refer to in a linear relationship?

The vertical change between any two points on a line. Signup and view all the answers

What does 'run' refer to in a linear relationship?

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

What is direct variation?

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

What is the constant of variation?

A constant ratio in a direct variation. Signup and view all the answers

What is the constant of proportionality?

The constant ratio in a proportional linear relationship. Signup and view all the answers

What is point-slope form?

An equation in the form of y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on a non-vertical line. Signup and view all the answers

What is slope-intercept form?

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

What is standard form?

An equation written in Ax + By = C form. Signup and view all the answers

What does x-intercept refer to?

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

What does y-intercept refer to?

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

Study Notes

Linear Relationships

Represented graphically by a straight line indicating a constant relationship between two quantities.

Constant Rate of Change

The change between any two points in a linear relationship remains the same across the graph.

Unit Rate

A specific type of rate or ratio where the denominator equals one, simplifying comparisons.

Slope

Measures the steepness of a line, defined as the ratio of vertical change (rise) to horizontal change (run).

Rise

The vertical distance between any two points on the line, indicating how much the y-value changes.

Run

The horizontal distance between two points on the line, indicating how much the x-value changes.

Direct Variation

Describes a relationship where two variable quantities maintain a consistent ratio.

Constant of Variation

The constant ratio found within a direct variation, signifying the relationship strength.

Constant of Proportionality

The constant ratio in proportional linear relationships, symbolizing direct proportionality between variables.

Point-Slope Form

Form of linear equation expressed as y - y1 = m(x - x1), where m indicates slope and (x1, y1) is a specific point on the line.

Slope-Intercept Form

Linear equation format written as y = mx + b, where m represents slope and b represents the y-coordinate where the line intersects the y-axis.

Standard Form

Linear equations structured as Ax + By = C, where A, B, and C are constants.

x-intercept

The specific x-coordinate at which the line intersects the x-axis, determined by setting y to zero in the equation.

y-intercept

The specific y-coordinate at which the line intersects the y-axis, determined by setting x to zero in the equation.

Description

Test your understanding of proportional relationships and slope with these flashcards. This quiz covers key terms such as linear relationships, constant rate of change, unit rate, and slope. Ideal for students mastering algebra concepts.