Question

Составить опорный конспект линейная функция

Answer 1

Линейной называется функция вида у=кх+в, где "к"-угловой коэффициент, определяющий угол наклона графика функции (прямой) к положительному направлению оси ОХ (если "к" - число положительное, то угол наклона острый, "к"-отрицательное - угол тупой). Коэффициент "в" определяет на сколько единиц график функции у=кх (график проходит через начало координат под углом 45 градусов) сдвигается от 0 вдоль оси ОУ параллельно самому себе вверх при "в" положительном, и вниз -  при "в" отрицательном.

Answer 2

Linear Function: Overview

A linear function is a fundamental concept in mathematics and is represented by an equation of the form y = mx + b, where: - y represents the dependent variable, - x represents the independent variable, - m is the slope of the line, and - b is the y-intercept.

Characteristics of Linear Functions

1. Slope (m): - The slope of a linear function represents the rate of change of the dependent variable with respect to the independent variable. - It is calculated as the ratio of the change in the y-variable to the change in the x-variable.

Source: 2. Y-Intercept (b): - The y-intercept is the point where the graph of the function intersects the y-axis. - It represents the value of the dependent variable when the independent variable is zero.

Source: 3. Graphical Representation: - The graph of a linear function is a straight line. - It can have a positive, negative, or zero slope, and the line can intersect the y-axis at any point.

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Applications of Linear Functions

Linear functions have numerous applications in various fields, including: - Economics: Modeling supply and demand curves. - Physics: Describing motion and forces. - Engineering: Analyzing electrical circuits and mechanical systems. - Finance: Calculating interest and depreciation.

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Conclusion

In summary, a linear function is a mathematical concept represented by an equation in the form of y = mx + b, where m is the slope and b is the y-intercept. Understanding linear functions is crucial for analyzing relationships between variables and has wide-ranging applications in different disciplines.