Questions and Answers
What is the definition of a graph?
What is a linear equation?
A line with a constant slope.
What is a non-linear equation?
A curve with an ever-changing slope.
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?
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In the equation y = mx + b, y and x are constants.
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When does the y-intercept occur?
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What two things do you need to graph a linear equation?
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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)?
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What are the classifications of lines by slope?
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How is the slope of a line written?
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What is the form of a vertical line?
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What is the form of a horizontal line?
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How do you graph using the x and y intercepts?
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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
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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.
