Friday, June 25, 2010

Linear equation

Let Us Learn About Linear Equation
Determining Linear equations had done by verifying weather; it may have one or more variables in the given linear equation. Linear equations occur with great reliability in applied mathematics. While they occur quite naturally when modeling many phenomena, they are mostly useful since many non-linear equations may be compact to linear equations by pretentious that quantities of interest vary to only a small extent from some "background" state.

Procedure to Determine Linear Equation

For determining linear equations “The simplest meaning of a linear equation is as a relationship between two variables that, when graphed against Cartesian axes, produces a straight line”.
The simplest definition's form for determining linear equations are done when y = mx + b. The "m" and "b" are the two constants. Represented on the x and y plane, where "m" refers to the slope of the equation and "b" refers to the point on the line of the equation hits the y-axis.
Linear equations are not usually distinct to constrict the equation to a pair of variables. For example, w + x + y + z = 3 is a linear equation as well as the equation x + xy + z = 3 however is not, because the xy terms is second-order, not first-order.


Linear equation:
Linear equation is a line equation. The general form of linear equation is y = mx + b. In this linear equation, we have x and y variables, slope and y intercept. M letter is used for slope. B letter is used for y intercept.
Linear function:
Linear function is a function of linear equation. Here we use letter f for linear function. The general form of linear function is f(x) = mx + b. In this linear function, we have m and b are constants and m is not equal to zero.
Let us see other concepts about linear equation and linear function.

Linear Equation:

Now we will see about some concept for linear equation.
X intercept:
X intercept is a point which is in x axis. The form of x intercept is (a , 0). Here a is x intercept.
Steps to find x intercept for linear equation:
In a linear equation, we set y equals zero, then we find x intercept.
A sentence of equality involving a single variable with highest power 1, is called a linear equation in that variable. A linear equation in one variable has a single unknown quantity called a variable represented by a letter.
E.g. ‘x’, where x has always power 1 and no x² or x³ etc.
Solving of an equation is the series of steps followed to find the value of the variable in the given equation. An equation is a statement that two quantities are equivalent.
For e.g.: x+2= 5, this linear equation means that when two is added to ‘x’ the unknown, the answer is 5.
While solving a linear equation, we follow a series of steps by applying addition, multiplication, subtraction or division operations on both sides of the equation by numbers and variables, so that we get a single variable on one side and a number on the other side.
Whatever we do toan equation, we need to do the SAME thing on BOTH Sides to arrive to the right solution!

Example 1: Solve for x, x+3= 6
Solution :
We need to isolate ‘x’
So, subtract on both sides with 3
x + 3 = 6
- 3 -3 (Same operation done on both sides with the same number !)
x +0 = 6-3 ( zero added to any number gives thesame number!)
x = 3 Answer
Checking:
Given equation: x+3 = 6
Left hand side = x+3, where x = 3( plug in this value)
(LHS) = 3+3
= 6 = Right hand side (RHS)
LHS = RHS, the answer x = 3 is right solution!
Example2 : Solve 3x+5 = 5x-11
Solution:
Given equation : 5x+5 = 3x+11
We have ‘x’ on both sides, combine the like terms
For that, let us subtract on both sides 3x.
Subtracting 3x on both sides
5x +5 = 3x+11
-3x -3x
_________________
(5-3)x +5 = 0+11
___________________
We need to eliminate 5 to isolate 2x, subtract 5 on both sides
2x +5 = 11
-5 -5
_________
2x +0 = 6
_________
2x = 6 (operation here is multiplication!)
Divide on both sides with 2 to isolate ‘x’
2x/2 = 6/2
x = 3 Answer
Checking:
LHS = 5x+5 = 5 (3) +5 = 15+5 = 20
RHS = 3x+11 = 3(3) +11 = 9+11= 20
LHS = RHS, the solution is right!
The homework assistance algebra is branch of mathematics
deals with calculations consists of equations. Symbols in an homework assistance algebraic expression are called variables of expression.If variables in homework assistance algebraic term are replaced with exact numbers, then expression yields a number which is called a value. If two homework assistance algebraic expressions are solved, get homework assistance algebraic equations.

Linear Equations

A set of linear equations having a regula solution set is called system of coincidents linear equations.Find values of three unknowns, given three linear equations in the three unknown v
ariables. Linear equation in three unknowns x, y, z is report of parity of form ax + by + cz + d = 0 where a, b, c, d are real numbers with a ≠ 0, b ≠ 0 and c ≠ 0.
Solve two equations in x, y
  • Two equations are given.
  • Removing y variable.
  • Substitute value of x in any one of two equations
  • Solve them in the usual way.
  • Thus the values of x and y are obtained.

Introduction to linear graph solver:
Algebra is one of the most basic element of mathematics in which, we
switch from basic arithmetic to variables. Algebra has various subdivisions like polynomials, graphing, system of equations, logarithms, etc. Sketching graphs for algebra equations or function is also a part of algebra. Graphing is nothing but the pictorial view of the given function or equation. Linear graph solver and method to use linear graph solver is given in the following sections.

Linear Equation:

Linear equations represent a straight line and it may be inclined or horizontal. The general format for a linear equation is as follows,
y = mx +b
where, m = slope of the line (it is a number)

Typical Linear Graph Solver:

A typical linear graph solver shown below,


Procedure to Use Linear Graph Solver:

The procedure to use the linear graph solver is shown below,
Step 1: Check whether the linear equation is a function of 'x' or 'y'.
Step 2: If it is a function of 'x' then enter the function in the first text box.
Step 3: If it is a function of 'y' then enter the function in the second text box.
Step 4: Then press enter button.

Working of a Linear Graph Solver:

once the enter button is pressed the linear solver accepts the linear equation given by the user and performs the following operations on it.
Step 1: The the given equation is y =ax+c. or x = ay +c.
Step 2: Assume first type y =ax+c. Since the given equation is a function of x, let y =f(x).
Step 3: Therefore f(x) = ax+c.
Step 4: It substitutes various values for ‘x’ and finds the corresponding value of f(x).
Step 5: It tabulates the values as columns x & f(x). The values of x as -2, -1, 0, 1, 2, 3 and for f(x), their corresponding values.
Step 6: The values in the table are the co-ordinates,
Step 7: It graphs the point and then joins them to give the graph
.

Example Problem to Use Linear Graph Solver:

Graph the linear equation y = 7x-9, The above equation is entered into the linear graph solver in the following format,


The solver receives the linear equation and performs the above said i =o perations and gives the graph output as shown below,

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