Algebra 1 Chapter 3 Flashcards

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Questions and Answers

What is the x-intercept?

The point where line crosses x-axis when y equals zero.

What is the slope-intercept form?

A linear equation written in the form y = mx + b.

Define a linear equation.

An equation whose solutions form a straight line on a coordinate plane.

What is a positive slope?

When a line goes up and to the right. Signup and view all the answers

What is a negative slope?

When a line goes down and to the right. Signup and view all the answers

Define a zero slope.

The slope of a horizontal line parallel to the x-axis. Signup and view all the answers

Define an undefined slope.

The slope of a vertical line parallel to the y-axis. Signup and view all the answers

What is a function?

An input-output relationship that has exactly one output for each input. Signup and view all the answers

Define slope.

Rise over run or change in y over change in x. Signup and view all the answers

What is the y-intercept?

Where a line crosses the y-axis when x equals zero. Signup and view all the answers

What does 'm' stand for in the equation y = mx + b?

The slope of the line. Signup and view all the answers

What does 'b' stand for in the equation y = mx + b?

The y-intercept of the line. Signup and view all the answers

What is the slope of the line represented by y = 3x + 2?

m = 3. Signup and view all the answers

What is the y-intercept of the line represented by y = 6x + 5?

b = 5. Signup and view all the answers

Define a linear function.

A function with ordered pairs that satisfy a linear equation. Signup and view all the answers

Define standard form of a linear equation.

Ax + By = C, where A ≥ 0 and is a whole number. Signup and view all the answers

What is an arithmetic sequence?

A numerical pattern that increases or decreases at a constant rate. Signup and view all the answers

What is 'd' in an arithmetic sequence?

The common difference. Signup and view all the answers

Study Notes

Key Algebra Concepts

x-intercept: Point where a graph crosses the x-axis; occurs when y equals zero.
slope-intercept form: Linear equation format is y = mx + b, where m is the slope and b is the y-intercept.
linear equation: Equation producing a straight line on the coordinate plane.
positive slope: Describes a line that rises as it moves from left to right.
negative slope: Describes a line that falls as it moves from left to right.
zero slope: Characterizes a horizontal line that has no change in y; represented as y = constant.
undefined slope: Applies to vertical lines which do not change x; represented as x = constant.

Functions and Relationships

function: Input-output relationship ensuring one output exists for each input.
slope: Ratio of vertical change (rise) to horizontal change (run); indicates the rate at which y changes with respect to x.
y-intercept: The point where a graph intersects the y-axis; occurs when x equals zero.

Equation Forms and Interpretations

standard form: Linear equation format is Ax + By = C, where A and B are not zero and A is a whole number.
linear function: A function characterized by ordered pairs adhering to a linear equation.
parent function: The simplest linear function defined by f(x) = x.

Slope and Intercept Calculations

Example slopes from specific equations:
- For y = 3x + 2, the slope is 3.
- For y = -2x - 8, the slope is -2.
To find y-intercepts:
- For y = 6x + 5, the y-intercept is 5.
- For y = 2x - 9, the y-intercept is -9.
For the equation 5x - 20y = 60, the slope is 1/4 and the y-intercept is -3.

Special Types of Variation

direct variation: Expressed as y = kx, where k is the constant of proportionality and cannot be zero.
constant of variation: The steady rate of change in direct variation, represented as k.

Sequences and Reasoning

sequence: An ordered list of numbers following a particular pattern.
arithmetic sequence: A sequence with a constant difference between consecutive terms, denoted as "d".
inductive reasoning: Drawing conclusions based on observed patterns from examples.

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Description

Test your knowledge with these flashcards covering key concepts from Algebra 1, Chapter 3. Learn crucial definitions such as x-intercept, slope-intercept form, and linear equations. Perfect for quick revision or preparation for exams.