Algebra 1 Chapter 5 Flashcards

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Questions and Answers

What is the slope?

The steepness of a line on a graph, equal to its vertical change divided by its horizontal change.

What is the slope-intercept form of a linear equation?

y = mx + b

What does 'rise' refer to in the context of a graph?

The difference in the y-values of two points on a line/The line's vertical change.

What does 'run' refer to in the context of a graph?

The difference in the x-values of two points on a line/The line's horizontal change. Signup and view all the answers

What is the standard form of a linear equation?

Ax + By = C Signup and view all the answers

What is the point-slope form of a linear equation?

y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line is passing through. Signup and view all the answers

What is the rate of change?

Change in the dependent variable divided by the change in the independent variable. Signup and view all the answers

What are parallel lines?

Lines in the same plane that do not intersect. Signup and view all the answers

What are perpendicular lines?

Two lines that intersect to form a right angle. Signup and view all the answers

What is the x-intercept?

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

What is the y-intercept?

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

What are opposite reciprocals?

Two numbers whose product is -1. Signup and view all the answers

What is a line of best fit?

A line that is very close to most of the data points in a scatter plot. Signup and view all the answers

What is a scatter plot?

A graph with points plotted to show a possible relationship between two sets of data. Signup and view all the answers

What is a positive correlation?

A relationship between two variables in which both variables either increase or decrease together. Signup and view all the answers

What is a negative correlation?

A relationship between increases in one variable and decreases in another. Signup and view all the answers

What is the slope formula?

Signup and view all the answers

What is direct variation?

A linear relationship that can be modeled with y = kx. Signup and view all the answers

What is an ordered pair?

A pair of numbers (x, y) that can be used to represent a point on a coordinate plane. Signup and view all the answers

What is a parent function?

The simplest of functions in a family. Signup and view all the answers

What is a translation in the context of graphing?

A shift of a graph horizontally, vertically, or both. Signup and view all the answers

Study Notes

Slope and Linear Equations

Slope indicates the steepness of a line, calculated as vertical change (rise) over horizontal change (run).
Slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b the y-intercept.
Standard form of a linear equation is written as Ax + By = C, where A, B, and C are constants.

Changes and Relationships in Graphs

Rise measures the vertical change between two points on a line, while run measures the horizontal change.
Rate of change is defined as the change in the dependent variable divided by the change in the independent variable.

Line Properties

Parallel lines never intersect and have the same slope.
Perpendicular lines intersect at right angles, with slopes that are opposite reciprocals.

Intercepts and Correlations

The x-intercept is where the graph crosses the x-axis, represented by the x-coordinate.
The y-intercept is where the graph crosses the y-axis, represented by the y-coordinate.
Positive correlation indicates that both variables increase or decrease together, while negative correlation indicates an increase in one variable and a decrease in another.

Data Representation

The line of best fit closely follows the data points in a scatter plot, helping to identify relationships between two datasets.
A scatter plot visually represents possible correlations between two variable sets.

Function Relationships

Direct variation models a linear relationship defined by the equation y = kx, where k is a constant.
An ordered pair (x,y) is used to represent specific points on a coordinate plane.
The parent function represents the simplest form within a family of functions.

Graph Transformations

Translation refers to the horizontal or vertical shifting of a graph, changing its position without altering its shape.

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Description

Test your understanding of slope and the constant rate of change with these flashcards from Algebra 1 Chapter 5. Each card covers key terms like slope, slope-intercept form, rise, and run in a clear and concise manner. Perfect for quick study and review!