Questions and Answers
What does 'Ordered Pairs' represent?
What is the definition of Slope?
The steepness of a line on a graph
What does Positive slope indicate?
Points up
What does Negative slope indicate?
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What is an Undefined slope?
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What does Zero slope indicate?
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What is the formula to calculate slope?
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What is the Y-intercept?
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What is the X-intercept?
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What is the Slope-Intercept Form of a line?
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What does the Domain of a graph represent?
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What does the Range of a graph represent?
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What is the Standard Form of a linear equation?
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What does HOY stand for?
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What does VUX stand for?
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What is the definition of Slope?
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What does 'Rise over run' mean in relation to slope?
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What is the Y-intercept commonly referred to as?
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What is the Linear Parent Function?
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In the equation y = mx + b, which term represents a point on the graph?
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What does 'Linear' refer to in mathematics?
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What does 'Nonlinear' refer to in mathematics?
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Study Notes
Ordered Pairs
- Represents a point on the graph using coordinates in the format (x, y).
Slope
- Indicates the steepness of a line, representing the rate of change between two points.
Positive Slope
- A line with a positive slope rises from left to right, indicating a direct relationship.
Negative Slope
- A line with a negative slope descends from left to right, indicating an inverse relationship.
Undefined Slope
- Occurs with vertical lines, where the slope cannot be quantified.
Zero Slope
- Associated with horizontal lines, indicating that there is no change in the y-values.
Formula to Calculate Slope
- Slope (m) is calculated using the formula m = (y₂ - y₁) / (x₂ - x₁).
Y-Intercept
- The point where the line intersects the y-axis, representing the value of y when x equals zero.
X-Intercept
- The point where the line intersects the x-axis, representing the value of x when y equals zero.
Slope-Intercept Form
- Represents a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Domain
- Refers to all possible x-values that a function can take.
Range
- Represents all possible y-values that a function can produce.
Standard Form
- A linear equation represented as Ax + By = C, where A, B, and C are constants. Use the cover-up method to find intercepts.
HOY (Horizontal Line)
- Indicates a horizontal line with a zero slope, can be represented as y = # (constant).
VUX (Vertical Line)
- Denotes a vertical line with an undefined slope, can be represented as x = # (constant).
Slope Characteristics
- The slope is the rate of change, serving as a coefficient in the linear equation.
- Can also be defined as "rise over run," illustrating the vertical change over horizontal change.
Linear Parent Function
- The simplest linear function given by y = x or f(x) = x, representing a straight line through the origin.
Y-Intercept in Context
- In the slope-intercept form, b represents the y-intercept. For example, in y = 2x + 3, b is 3, representing the point (0, 3).
Linear vs Nonlinear Functions
- Linear functions produce straight lines, while nonlinear functions result in curves or other shapes.
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Description
Enhance your understanding of slope concepts with these flashcards. Each card outlines key terms such as ordered pairs, positive and negative slopes, and their definitions. Perfect for Algebra 1 students looking to reinforce their knowledge.
