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  2. Linear equation - Wikipedia

    en.wikipedia.org/wiki/Linear_equation

    Conversely, every line is the set of all solutions of a linear equation. The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding ...

  3. Linear function (calculus) - Wikipedia

    en.wikipedia.org/wiki/Linear_function_(calculus)

    A linear function is a polynomial function in which the variable x has degree at most one: [2] = +. Such a function is called linear because its graph, the set of all points (, ()) in the Cartesian plane, is a line. The coefficient a is called the slope of the function and of the line (see below).

  4. Linear function - Wikipedia

    en.wikipedia.org/wiki/Linear_function

    In mathematics, the term linear function refers to two distinct but related notions: [1] In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. [2] For distinguishing such a linear function from the other concept, the term affine function is often used ...

  5. Log–log plot - Wikipedia

    en.wikipedia.org/wiki/Log–log_plot

    A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).

  6. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as:

  7. Line (geometry) - Wikipedia

    en.wikipedia.org/wiki/Line_(geometry)

    Line graphs of linear equations on the Cartesian plane . ... is the set of all points whose coordinates (x, y) satisfy a linear equation; that is, = {(,) ...

  8. Piecewise linear function - Wikipedia

    en.wikipedia.org/wiki/Piecewise_linear_function

    The graph of this function is shown to the right. Since the graph of an affine(*) function is a line, the graph of a piecewise linear function consists of line segments and rays. The x values (in the above example −3, 0, and 3) where the slope changes are typically called breakpoints, changepoints, threshold values or knots. As in many ...

  9. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set. For linear equations, logical independence is the same as linear independence. The equations x − 2y = −1, 3x + 5y = 8, and 4x + 3y = 7 are linearly dependent. For example ...

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