Expalnation:
Linear equation
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the
first power of) a single variable.
Linear equations can have one or more variables. Linear equations
occur with great regularity in applied
mathematics. While they arise quite naturally when modeling many phenomena,
they are particularly useful since many non-linear
equations may be reduced to
linear equations by assuming that quantities of interest vary to only a small extent
from some "background" state.
Linear
equations in two variables
A common form of a linear equation in the two variables x and y is
where m and b designate constants. The origin of the name "linear"
comes from the fact that the set of solutions of such an equation forms a straight line in the plane. 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.
Since terms of linear equations cannot contain products of
distinct or equal variables, nor any power (other than 1) or other function of
a variable, equations involving terms such as xy, x^{2},y^{1/3},
and sin(x) are nonlinear.
Forms for 2D linear equations
Linear equations can be rewritten using the laws of elementary algebra into several different
forms. These equations are often referred to as the "equations of the
straight line". In what follows x, y, t and θ are variables; other letters represent constants (fixed numbers).
General form
where A and B are not both equal to zero. The
equation is usually written so that A ≥ 0, by convention. The graph of the equation is a straight line, and every straight line
can be represented by an equation in the above form. If A is nonzero, then the x-intercept, that is, the x-coordinate of the point where the graph crosses
the x-axis (where, y is zero), is −C/A.
If B is nonzero, then the y-intercept, that is the y-coordinate of the point where
the graph crosses the y-axis
(where x is zero), is −C/B, and the slope of the line is −A/B. (Our
solved example in mathguru.com uses this concept).
http://en.wikipedia.org/wiki/Linear_equation#Linear_equations_in_two_variables
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