Questions and Answers
What is the y-intercept in the equation of a straight line?
What are x-intercepts?
Points on the graph where y is zero.
Define domain in the context of a function.
The set of values of the independent variable(s) for which a function or relation is defined.
What does range refer to in a set of values?
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What characterizes a linear equation?
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Give a brief description of a non-linear system.
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What is a linear function?
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What does a constant rate of change imply in mathematics?
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What is the slope of a line?
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Study Notes
Slope Intercept Key Terms
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Y-Intercept: Part of the linear equation represented as y = mx + b, where 'b' signifies the y-value at the point where the line intersects the y-axis.
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X-Intercept: Represents points where the graph crosses the x-axis (y = 0). These points occur when the value of y is zero.
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Domain: Refers to the set of valid values for the independent variable(s) that result in real outputs (y-values) for a function. Typically includes all x-values that yield real y-values.
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Range: Defined as the difference between the maximum and minimum values in a dataset. It can also encompass all output values of a function, representing the span of values a function can produce.
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Linear Equation: An algebraic expression where each term consists of a constant or the product of a constant and the first power of a single variable. Linear equations are foundational in mathematics and often appear in various mathematical disciplines.
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Non-linear Function: Characterized by equations where the unknowns are part of a polynomial of degree greater than one. Non-linear functions do not produce straight-line graphs.
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Linear Function: A specific type of function whose graph is a straight line. Algebraically, it is defined as a polynomial of degree one or a constant horizontal line (y = c).
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Constant Rate of Change: Indicates no acceleration; a function exhibiting this trait has a second derivative of zero. Graphically, it appears as a straight line, with a uniform change in y corresponding to changes in x.
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Slope: Represents the steepness of a line defined by the rise over run between two points. Various formulas exist to calculate slope, illustrating its significance in determining line steepness in geometry and algebra.
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Description
Explore the fundamental concepts of slope and intercepts in linear equations with this flashcard quiz. Understand the definitions of y-intercept and x-intercept, and learn how they are represented in the linear equation y = mx + b.