Linear B

(noun)

A syllabic script that was used for writing Mycenaean Greek— the earliest attested form of Greek.

Related Terms

  • Neopalatial period
  • Minoan civilization
  • Knossos
  • Linear
  • polis
  • synoecism
  • oikoi
  • palace economy
  • Linear A

(noun)

Syllabic script that was used for writing Mycenaean Greek, the earliest documented form of the Greek language.

Related Terms

  • Neopalatial period
  • Minoan civilization
  • Knossos
  • Linear
  • polis
  • synoecism
  • oikoi
  • palace economy
  • Linear A

Examples of Linear B in the following topics:

  • Linear Equations

    • A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable.
    • A common form of a linear equation in the two variables $x$ and $y$ is:
    • where $m$ and $b$ designate constants.
    • In this particular equation, the constant $m$ determines the slope or gradient of that line, and the constant term $b$ determines the point at which the line crosses the $y$-axis, otherwise known as the $y$-intercept.
    • Linear differential equations are of the form:
  • Linear and Quadratic Functions

    • In calculus and algebra, the term linear function refers to a function that satisfies the following two linearity properties:
    • Linear functions may be confused with affine functions.
    • One variable affine functions can be written as $f(x)=mx+b$.
    • However, the term "linear function" is quite often loosely used to include affine functions of the form $f(x)=mx+b$.
    • Linear functions form the basis of linear algebra.
  • The Equation of a Line

    • In statistics, linear regression can be used to fit a predictive model to an observed data set of $y$ and $x$ values.
    • In statistics, simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable.
    • A common form of a linear equation in the two variables $x$ and $y$ is:
    • Where $m$ (slope) and $b$ (intercept) designate constants.
    • In this particular equation, the constant $m$ determines the slope or gradient of that line, and the constant term $b$ determines the point at which the line crosses the $y$-axis, otherwise known as the $y$-intercept.
  • Linear and Quadratic Equations

    • The constants $a$, $b$, and $c$ are respectively called the quadratic coefficient, the linear coefficient, and the constant term (or free term).
    • $\displaystyle x=\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2a }$
    • $\displaystyle x=\frac { -b + \sqrt { { b }^{ 2 }-4ac } }{ 2a }$
    • $\displaystyle x=\frac { -b- \sqrt { { b }^{ 2 }-4ac } }{ 2a }$
    • Graph sample of linear equations, using the y=mx+b format, as seen by $y=-x+5$(red) and $y=\frac{1}{2}x +2$ (blue).
  • Slope and Y-Intercept of a Linear Equation

    • For the linear equation y = a + bx, b = slope and a = y-intercept.
    • A linear equation that expresses the total amount of money Svetlana earns for each session she tutors is y = 25 + 15x.
    • The slope is 15 (b = 15).
    • (a) If b > 0, the line slopes upward to the right.
    • (b) If b = 0, the line is horizontal.
  • Linear Equations

    • Linear regression for two variables is based on a linear equation with one independent variable.
    • The graph of a linear equation of the form y = a + bx is a straight line.
    • Linear equations of this form occur in applications of life sciences, social sciences, psychology, business, economics, physical sciences, mathematics, and other areas.
  • What is a Linear Function?

    • For example, a common equation, $y=mx+b$, (namely the slope-intercept form, which we will learn more about later) is a linear function because it meets both criteria with $x$ and $y$ as variables and $m$ and $b$ as constants.  
    • In the linear function graphs below, the constant, $m$, determines the slope or gradient of that line, and the constant term, $b$, determines the point at which the line crosses the $y$-axis, otherwise known as the $y$-intercept.
    • Horizontal lines have a slope of zero and is represented by the form, $y=b$, where $b$ is the $y$-intercept.  
    • The blue line, $y=\frac{1}{2}x-3$ and the red line, $y=-x+5$ are both linear functions.  
    • Identify what makes a function linear and the characteristics of a linear function
  • Solving Problems with Inequalities

    • A linear inequality is a mathematical statement that one linear expression is greater than or less than another linear expression.
    • Let a, b, and c represent real numbers and assume that a < b.
    • a + c < b + c and a − c < b − c.
    • If c is a positive real number, consider then if a < b, ac < bc and ac < bc.
    • If c is a negative real number, then if a < b, ac > bc and ac > bc.
  • Linear Approximation

    • A linear approximation is an approximation of a general function using a linear function.
    • In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function).
    • Linear approximations are widely used to solve (or approximate solutions to) equations.
    • Linear approximation is achieved by using Taylor's theorem to approximate the value of a function at a point.
    • If one were to take an infinitesimally small step size for $a$, the linear approximation would exactly match the function.
  • Linear Equations and Their Applications

    • Linear equations are those with one or more variables of the first order.
    • There is in fact a field of mathematics known as linear algebra, in which linear equations in up to an infinite number of variables are studied.
    • Linear equations can therefore be expressed in general (standard) form as:
    • where a, b, c, and d are constants and x, y, and z are variables.
    • Imagine these linear equations represent the trajectories of two vehicles.
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