Linear Equations
A linear equation is a very interesting and important part of the algebra. It is essentially an algebraic equation which is consisting of a term that can be a single variable and constant or product of constants. It may have more than one variable. In general we can define a Linear Equations in terms of two variables say x, y and two designate constants c and m, which has a form: y = mx + c. Here the m defines the slope of the equation of line.
So we can say that a linear equation is a mathematical expression with an equal sign and a linear equation. A linear expression is one which is a mathematical statement that performs operations such addition, subtraction, division and multiplication.
In a linear equation the variables used are unknowns and they cannot be in one of the following forms:
1. In a linear equation the variable cannot have an exponent.
2. It also not found under square or any other root.
3. It cannot multiply and divide each other like x / y or y / x.
If this linear equation is in 2 dimensional then it can be written as Ax + By + C = 0. Here A and B are non zero and C can be zero or not.
The standard form of the equation is Ax + By =C.
The slope intersect form of the linear equation can be written as y =mx + c.
In case of point slope the equation has a form y – y1 = m(x – x1). Here (x1, y1) is any point on line.
The two point form of the linear equation is y – y1 = [ (y2 – y1) / (x2 – x1)] * (x - x1). Here (x1, y1) and (x2, y2) are two points on the line and x2 is not equals to x1. And the slope is given as
m =(y2 – y1) / (x2 – x1).
The parametric form of the linear equation is x =T*t + Q and y = V*t + R. Here the variable parameter is t, with a slope m that is equal to V/T with x intercept
(VQ - TR) / V and the y intercept is (RT - VQ) / T.
The linear equation also has an intercept form according to which it is defined as x/a + y/b =1, where a and b are non zero.
A linear equation can also be written with more than two variables. The general equation is
a1x1 + a2x2 + a3x3+………………..+ anxn = b. Here n is the total number of variables.
In the above equation a1, a2, a3,…….., an are the coefficients and x1, x2,…….., xn are the variables and b is a constant. If we write the equation with three variables then we will replace x1 by x, x2 by y and x3 by z.
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