Podcast
Questions and Answers
What is the definition of a graph?
What is the definition of a graph?
What is a linear equation?
What is a linear equation?
A line with a constant slope.
What is a non-linear equation?
What is a non-linear equation?
A curve with an ever-changing slope.
What is a table of values in relation to an equation?
What is a table of values in relation to an equation?
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What is the slope-intercept form of the equation of a line?
What is the slope-intercept form of the equation of a line?
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In the equation y = mx + b, y and x are constants.
In the equation y = mx + b, y and x are constants.
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When does the y-intercept occur?
When does the y-intercept occur?
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What two things do you need to graph a linear equation?
What two things do you need to graph a linear equation?
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What does it mean for points to be collinear?
What does it mean for points to be collinear?
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What is the slope formula for a non-vertical line passing through points (x1, y1) and (x2, y2)?
What is the slope formula for a non-vertical line passing through points (x1, y1) and (x2, y2)?
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What are the classifications of lines by slope?
What are the classifications of lines by slope?
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How is the slope of a line written?
How is the slope of a line written?
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What is the form of a vertical line?
What is the form of a vertical line?
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What is the form of a horizontal line?
What is the form of a horizontal line?
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How do you graph using the x and y intercepts?
How do you graph using the x and y intercepts?
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What is the usefulness of slope-intercept form?
What is the usefulness of slope-intercept form?
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Study Notes
Graph Concepts
- A graph represents a set of solutions (x, y) that satisfy an equation.
- Linear equations produce straight lines with constant slopes, while non-linear equations yield curves with varying slopes.
Key Definitions
- Table of Values: A collection of ordered pairs representing solutions to an equation.
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Slope-Intercept Form: The equation of a line is written as ( y = mx + b ) where:
- ( m ) is the slope,
- ( b ) is the y-intercept.
Intercepts
- Y-Intercept: Occurs when ( x = 0 ); represented as the point (0, b).
- X-Intercept: Found by setting ( y = 0 ) in the equation.
Graphing Techniques
- To graph a linear equation, determine the position (any point on the line) and direction (slope).
- Steps for graphing using slope-intercept form:
- Ensure equation is in slope-intercept form.
- Plot the y-intercept on the coordinate plane.
- Use the slope to find additional points:
- Slope in fraction form indicates movement (up/down for the numerator, right/left for the denominator).
Lines and Slopes
- Points are collinear if they lie on the same line with identical slopes.
- The slope formula: For points (x1, y1) & (x2, y2), slope ( m = \frac{y2 - y1}{x2 - x1} ).
- Classifications of lines by slope:
- Positive slope: Rises from left to right.
- Negative slope: Falls from left to right.
- Zero slope: Horizontal line.
- Undefined slope: Vertical line.
Line Equations
- Vertical Line: Written as ( x = a ) where all coordinates have the same value.
- Horizontal Line: Written as ( y = b ) where all y-values are constant.
Using Intercepts for Graphing
- Find the x-intercept by setting ( y = 0 ) and solve for ( x ).
- Find the y-intercept by setting ( x = 0 ) and solve for ( y ).
- Plot both intercepts and connect them with a line, adding arrowheads for direction.
Slope-Intercept Utility
- The slope-intercept equation ( y = mx + b ) is vital for:
- Sketching graphs,
- Determining the slope,
- Identifying the y-intercept of a line.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of key concepts in graphing from Algebra 1, Unit 4. This set of flashcards covers essential terms such as graph, linear equations, and non-linear equations, along with definitions to help reinforce your knowledge. Ideal for quick revision and self-assessment.
