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Needed a Document for linear equation in one variable? Related: L 6 ...
**Linear Equation in One Variable**

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where a and b are constants, and x is the variable. The goal is to find the value of x that satisfies the equation.

**Solving a Linear Equation**

To solve a linear equation in one variable, follow these steps:

1. Simplify the equation by combining like terms on each side of the equation.

2. Get rid of any coefficients by dividing both sides of the equation by the coefficient of the variable.

3. Isolate the variable by adding or subtracting constants to both sides of the equation.

4. Solve for the variable by performing the necessary operations.

5. Check your solution by substituting the value of the variable back into the original equation and verifying that both sides of the equation are equal.

**Example**

Let's solve the linear equation 2x - 5 = 7.

1. Simplify the equation:
2x - 5 + 5 = 7 + 5
2x = 12

2. Get rid of the coefficient by dividing both sides by 2:
2x/2 = 12/2
x = 6

3. The variable is already isolated, so we move to the next step.

4. The solution is x = 6.

5. Check the solution:
2(6) - 5 = 7
12 - 5 = 7
7 = 7

The value of x = 6 satisfies the given linear equation.

**Conclusion**

A linear equation in one variable is an equation that can be solved to find the value of the variable. By following the steps mentioned above, you can solve linear equations and find the solution. It is important to check your solution by substituting it back into the original equation to ensure its correctness. Linear equations in one variable are fundamental in mathematics and have various applications in real-life problem-solving.
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Needed a Document for linear equation in one variable? Related: L 6 ...
Linear Equations
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
What is a Linear Equation?
An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has a variable whose exponent is more than 1. The graph of a linear equation always forms a straight line.
Linear Equation Definition: A linear equation is an 
algebraic equation
 where each term has an 
exponent
 of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear' equation.
There are linear equations in one variable and linear 
equations
 in two variables. Let us learn how to identify linear equations and non-linear equations with the help of the following examples.
EquationsLinear or Non-Linear
y = 8x - 9Linear
y = x2 - 7Non-Linear, the power of the variable x is 2
√y + x = 6Non-Linear, the power of the variable y is 1/2
y + 3x - 1 = 0Linear
y2 - x = 9Non-Linear, the power of the variable y is 2
Linear Equation Formula
The 
linear equation formula
 is the way of expressing a linear equation. This can be done in different ways. For example, a linear equation can be expressed in the standard form, the slope-intercept form, or the point-slope form. Now, if we take the standard form of a linear equation, let us learn the way in which it is expressed. We can see that it varies from case to case based on the number of variables and it should be remembered that the highest (and the only) degree of all variables in the equation should be 1.
  • Slope intercept form of a linear equation is y = mx + c (where m = slope and c = y-intercept)
  • Point slope form of a linear equation is y - y
    1
     = m(x - x
    1
    ) (where m = slope and (x
    1
    , y
    1
    ) is a point on the line)
Note: The 
slope
 of a linear equation is the amount by which the line is rising or falling. It is calculated by the formula 
rise/run
. i.e., if (x
1
, y
1
) and (x
2
, y
2
) are any two points on a line then its slope is calculated using the formula (y
2
 - y
1
)/(x
2
 - x
1
).
Linear Equations in Standard Form
The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are 
real numbers
, and x is the single variable. The 
standard form of linear equations
 in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.


Linear Equation Graph
The 
graph of a linear equation
 in one variable x forms a 
vertical line
 that is parallel to the y-axis and vice-versa, whereas, the graph of a linear equation in two variables x and y forms a straight line. Let us graph a linear equation in two variables with the help of the following example.
Example: Plot a graph for a linear equation in two variables, x - 2y = 2.
Let us plot the 
linear equation graph
 using the following steps.
  • Step 1: The given linear equation is x - 2y = 2.
  • Step 2: Convert the equation in the form of y = mx + b. This will give: y = x/2 - 1.
  • Step 3: Now, we can replace the value of x for different 
    numbers
     and get the resulting value of y to create the coordinates.
  • Step 4: When we put x = 0 in the equation, we get y = 0/2 - 1, i.e. y = -1. Similarly, if we substitute the value of x as 2 in the equation, y = x/2 - 1, we get y = 0.
  • Step 5: If we substitute the value of x as 4, we get y = 1. The value of x = -2 gives the value of y = -2. Now, these pairs of values of (x, y) satisfy the given linear equation y = x/2 - 1. Therefore, we list the coordinates as shown in the following table.
x024-2
y-101-2
  • Step 6: Finally, we plot these points (4,1), (2,0), (0,-1) and (-2, -2) on a graph and join the points to get a straight line. This is how a linear equation is represented on a graph.

    Linear Equations in One Variable
    A linear equation in one variable is an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution. It is the easiest way to represent a mathematical statement. This equation has a 
    degree
     that is always equal to 1. A linear equation in one variable can be solved very easily. The variables are separated and brought to one side of the equation and the constants are combined and brought to the other side of the equation, to get the value of the unknown variable.
    Example: Solve the linear equation in one variable: 3x + 6 = 18.
    In order to solve the given equation, we bring the numbers on the right-hand side of the equation and we keep the variable on the left-hand side. This means, 3x = 18 - 6. Then, as we 
    solve for x
    , we get, 3x = 12. Finally, the value of x = 12/3 = 4.


  • Linear Equations in Two Variables
    A linear equation in two variables is of the form Ax + By + C = 0, in which A, B, C are real numbers and x and y are the two variables, each with a degree of 1. If we consider two such linear equations, they are called simultaneous linear equations. For example, 6x + 2y + 9 = 0 is a linear equation in two variables. There are various ways of 
    solving linear equations
     in two variables like the 
    graphical method
    , the 
    substitution method
    , the 
    cross multiplication method
    , the 
    elimination method
    , and the 
    determinant
     method.
    ☛Also check: 
    Linear Equations In Two Variables Worksheets
    How to Solve Linear Equations?
    An equation is like a weighing balance with equal weights on both sides. If we add or subtract the same number from both sides of an equation, it still holds true. Similarly, if we multiply or divide the same number on both sides of an equation, it is correct. We bring the variables to one side of the equation and the constant to the other side and then find the value of the unknown variable. This is the way to 
    solve a linear equation
     with one variable. Let us understand this with the help of an example.
    Example: Solve the equation, 3x - 2 = 4.
    We perform mathematical operations on the Left-hand side (LHS) and the right-hand side (RHS) so that the balance is not disturbed. So, let us add 2 on both sides to reduce the LHS to 3x. This will not disturb the balance. The new LHS is 3x - 2 + 2 = 3x and the new RHS is 4 + 2 = 6. Now, let us divide both sides by 3 to reduce the LHS to x. Thus, we have x = 2. This is one of the ways of solving linear equations in one variable.
    Tips on Linear Equations:
    • The value of the variable that makes a linear equation true is called the solution or 
      root
       of the linear equation.
    • The solution of a linear equation is unaffected if the same number is added, subtracted, multiplied, or divided into both sides of the equation.
    • The graph of a linear equation in one or two variables always forms a straight line.
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Needed a Document for linear equation in one variable? Related: L 6 : Questions 1 Pictographs) CBSE Class 6 Mathematics VI?
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