Questions and Answers
What is the slope formula?
What is the slope-intercept formula?
y = mx + b
What is the standard formula for a linear equation?
Ax + By = C
What are the steps for graphing linear equations?
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What are the 4 types of slopes?
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What is the rise in a linear equation?
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What is the run in a linear equation?
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If the slope is 2 and the y-intercept is (0, -1), what is it in slope-intercept form?
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When graphing a point, where should you put the point?
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What is the slope of the equation '3x - 2y = -14'?
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What is the y-intercept of the equation '3x - 2y = -14'?
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Study Notes
Slope Concepts in Algebra 1
- Slope Formula: Represents the rate of change; calculated using Y2-Y1/X2-X1.
- Slope-Intercept Formula: Used for linear equations; formatted as y=mx+b, where m is the slope and b is the y-intercept.
- Standard Form of Linear Equations: A common way to express linear equations, given as Ax + By = C, where A, B, and C are constants.
Graphing Linear Equations
- To graph linear equations, first convert to slope-intercept form.
- Start by plotting the y-intercept at the point (0,b).
- Use the slope to determine additional points, employing the rise/run method.
- Draw a line through the points using a ruler, adding arrows at both ends to indicate continuation.
Types of Slopes
- Positive Slope: Indicates that as x increases, y also increases.
- Negative Slope: Indicates that as x increases, y decreases.
- Zero Slope: Represented by a horizontal line, indicating no change in y as x varies.
- Undefined Slope: Associated with vertical lines, where x remains constant regardless of y.
Key Definitions
- Rise: Refers to the vertical change between two points on a graph.
- Run: Stands for the horizontal change between two points on a graph.
- Y-intercept for the equation "3x - 2y = -14" is found at (0, 7) after rearranging into slope-intercept form.
Slope-Intercept Form Example
- Given a slope of 2 and a y-intercept of (0, -1), the equation translates to y = 2x - 1.
Point Placement When Graphing
- When graphing a point, begin by placing it at the y-intercept.
Slope Calculation Example
- For the equation "3x - 2y = -14", the slope, after manipulation, is calculated as 3/2.
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Enhance your understanding of slopes with these flashcards. Each card defines key concepts like the slope formula, slope-intercept formula, and techniques for graphing linear equations. Perfect for Algebra 1 students looking to master slope-related topics.
