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alejandralyne0204
10/20/2023
Algebra 1
Understanding linear functions pt.2
Linear functions are fundamental mathematical concepts with constant rates of change. This guide provides a detailed explanation of linear functions with examples and answers, covering key topics like graphing, standard form, and real-world applications. Students will learn to identify, graph, and analyze linear function examples with solutions and graphs.
10/20/2023
104
This page focuses on the standard form of linear equations and provides examples of graphing linear functions.
Definition: The standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers, and A and B are not both zero.
The lesson provides an example of graphing the linear equation 5x + y = 10:
Example: To determine if a point (2,5) is on the graph of 5x + y = 10, substitute the values: 5(2) + 5 = 15 ≠ 10, so (2,5) is not on the graph.
Highlight: When graphing linear functions, it's important to note that A and B in the standard form cannot be zero simultaneously.
This page covers real-world applications of linear functions and introduces graphing techniques, including using intercepts.
Example: Sal's video store pricing model is represented by the function F(x) = 2x, where x is the number of DVDs purchased. This results in a discrete graph.
The lesson explains how to determine the domain and range of this function:
Highlight: When graphing discrete functions, use individual points rather than a continuous line.
The lesson introduces a problem about miners ascending in an elevator, which will be used to demonstrate graphing linear functions using intercepts in the next lesson.
Vocabulary: Intercepts are the points where a graph crosses the x-axis (x-intercept) or y-axis (y-intercept).
This comprehensive guide provides students with a solid foundation in understanding and working with linear functions, preparing them for more advanced mathematical concepts.
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Linear functions are fundamental mathematical concepts with constant rates of change. This guide provides a detailed explanation of linear functions with examples and answers, covering key topics like graphing, standard form, and real-world applications. Students will learn to identify, graph, and analyze linear function examples with solutions and graphs.
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This page focuses on the standard form of linear equations and provides examples of graphing linear functions.
Definition: The standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers, and A and B are not both zero.
The lesson provides an example of graphing the linear equation 5x + y = 10:
Example: To determine if a point (2,5) is on the graph of 5x + y = 10, substitute the values: 5(2) + 5 = 15 ≠ 10, so (2,5) is not on the graph.
Highlight: When graphing linear functions, it's important to note that A and B in the standard form cannot be zero simultaneously.
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This page covers real-world applications of linear functions and introduces graphing techniques, including using intercepts.
Example: Sal's video store pricing model is represented by the function F(x) = 2x, where x is the number of DVDs purchased. This results in a discrete graph.
The lesson explains how to determine the domain and range of this function:
Highlight: When graphing discrete functions, use individual points rather than a continuous line.
The lesson introduces a problem about miners ascending in an elevator, which will be used to demonstrate graphing linear functions using intercepts in the next lesson.
Vocabulary: Intercepts are the points where a graph crosses the x-axis (x-intercept) or y-axis (y-intercept).
This comprehensive guide provides students with a solid foundation in understanding and working with linear functions, preparing them for more advanced mathematical concepts.
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Linear functions are characterized by a constant rate of change between variables. This lesson introduces the concept of linear functions, their properties, and how to distinguish them from non-linear functions.
Definition: A linear function is a mathematical relationship where a constant change in one variable corresponds to a constant change in another variable.
The lesson emphasizes that all linear functions behave similarly and can be represented by linear equations with two variables. Examples of linear equations include:
Example: The equation y = x² is not a linear function because it does not have a constant change in y for a constant change in x.
Highlight: In linear equations, the highest exponent for x and y is always 1.
The lesson also introduces non-linear equations, such as:
Vocabulary: Non-linear functions are mathematical relationships where the rate of change between variables is not constant.
Average App Rating
Students use Knowunity
In Education App Charts in 17 Countries
Students uploaded study notes
iOS User
Stefan S, iOS User
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