Podcast
Questions and Answers
What is the x-intercept?
What is the x-intercept?
The point where line crosses x-axis when y equals zero.
What is the slope-intercept form?
What is the slope-intercept form?
A linear equation written in the form y = mx + b.
Define a linear equation.
Define a linear equation.
An equation whose solutions form a straight line on a coordinate plane.
What is a positive slope?
What is a positive slope?
What is a negative slope?
What is a negative slope?
Define a zero slope.
Define a zero slope.
Define an undefined slope.
Define an undefined slope.
What is a function?
What is a function?
Define slope.
Define slope.
What is the y-intercept?
What is the y-intercept?
What does 'm' stand for in the equation y = mx + b?
What does 'm' stand for in the equation y = mx + b?
What does 'b' stand for in the equation y = mx + b?
What does 'b' stand for in the equation y = mx + b?
What is the slope of the line represented by y = 3x + 2?
What is the slope of the line represented by y = 3x + 2?
What is the y-intercept of the line represented by y = 6x + 5?
What is the y-intercept of the line represented by y = 6x + 5?
Define a linear function.
Define a linear function.
Define standard form of a linear equation.
Define standard form of a linear equation.
What is an arithmetic sequence?
What is an arithmetic sequence?
What is 'd' in an arithmetic sequence?
What is 'd' in an arithmetic sequence?
Flashcards
x-intercept
x-intercept
The point where a graph crosses the x-axis. It occurs when y is zero.
slope-intercept form
slope-intercept form
A way to write linear equations: y = mx + b. 'm' is the slope, and 'b' is the y-intercept.
linear equation
linear equation
An equation whose graph is a straight line.
positive slope
positive slope
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negative slope
negative slope
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zero slope
zero slope
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undefined slope
undefined slope
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function
function
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slope
slope
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y-intercept
y-intercept
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standard form
standard form
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linear function
linear function
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parent function
parent function
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direct variation
direct variation
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constant of variation
constant of variation
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sequence
sequence
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arithmetic sequence
arithmetic sequence
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inductive reasoning
inductive reasoning
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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.
