Generally, linear equation is any equation that when graphed produces a straight line.
There are various types of equations; none except linear equations will produce a straight line when graphed.
A polynomial with variables of first degree that can be equated to zero is a linear equation.
i.e. ax + by + c = 0
Or
ax + by = c
where c is a constant
Example : 2x + 3y – 4 = 0
5x – 7y = -2
Linear Equation Properties
1. Linear equation occur with great regularity in applied mathematics.
2. Slope can be identified by linear equation.
How to Solve Linear Equation
When any linear equation is given, first one has to check whether it is a linear equation in one variable or linear equation in two variable. Depending upon that start to solve linear equation using following steps.
Step 1 : Consider the given linear equation.
Step 2 : Shift the constant terms to right hand side and retain terms with variables on left on side itself.
Step 3 : Perform the mathematical operation required on both the sides with like terms.
Step 4 : On solving linear equation, resultant will be the value of the variable
Below example will help to understand the steps clearly.
Example s of Linear Equation
Example 1: Convert the following equation in statement form.
x – 5 = 9
Solution :
5 taken from x gives 9
So x = 9 + 5 = 14
Hence x = 14
For verification of the statement,
x - 5 = 9
14 - 5 = 9
9 = 9 So left hand side value is equal to right hand side value.
Hence the value of x detemined is correct
Example 2 : Write the following statement in the form of equation
The sum of three times x and 11 is 32
Solution :
Three times x is 3x Sum of 3x and 11 is 3x + 11 .
The sum is 32 The equation is 3x + 11 = 32
Linear Equation in one-variable
Linear equation in one-variables consist of one variables having a degree 1 and equated to a constant. It is basically written in the form of
ax +b =0
where a, b is a real number and a can’t be equal to 0
Examples:
2x + 3 = 0
3 - 4y = 0
Linear equation in two-variable
Linear equation in two-variables consist of two variables having a degree 1 and equated to a constant. It is basically written in the form of aX + bY +C =0 where X and Y are the variables with degree 1 . and a ,b , c are the real numbers , such that a and b are not both zero.
Example s :
2x + 3y = 4
4x+7y=10
To Plot The Linear Equation Graph
- Re-write the given equation expressing one term in terms of the other.
Finding values to plot linear equations graph
Find at least 3 sets of values for the variables satisfying the equation.
2x+y=5
Express y in terms of x.
y=5-2x
Select three values of x, find corresponding values of y.
x=0, y=5-(2x0)=5
x=1, y=5-(2x1)=3
x=-1, y=5-(-2)=7
- Draw the x and y - axes. Choose a suitable scale so as to locate the selected point on the graph.
- Plot the selected points.
- Draw a straight line joining the points.
Linear Equations Graph Example
Plot the graph of 2x + 3y = 9.
Suggested Answer :
Plot the graph of
2x+3y=9
2x=9-3y
(Expressing one variable in terms of the other)
Put y = 1,
x=3
Put y = -1,
x=6
Put y = 7,
x=-6
