Graph of Linear Equation

How to represent a graph of linear equation in two variables?

Linear equation in two variables is represented graphically by the line whose points give the collection of solutions of the equation. This is called graphing linear equation.


Properties for graphing linear equation:

1. Linear equations have infinitely many solutions.

2. Every point (h, k) on the line AB gives the solution x = h and y = k.

3. Every point which lies on AB satisfies the equation of AB.

4. To draw an exact line on the graph paper you can plot as many points you like, but it is necessary to plot minimum three points.

Method to draw the graph of linear equation in two variables:

1. Convert the given equation in the form of y = mx + b (slope intercept form).

2. Apply trial and error method to find 3 pairs of values of (x, y) which satisfy the given equation.

3. Plot these points on the graph paper.

4. Join the points marked on the graph paper to get a straight line which represent the given equation graphically.


Note:

1. Linear equation in two variables has infinitely many solutions.

2. A graph of linear equation is always a straight line.

3. Every point on the straight line is the solution of the linear equation.

4. Equation of y-axis is x = 0. The standard form of this equation is x + 0.y = 0.

5. Equation of x-axis is y = 0. The standard form of this equation is 0.x + y = 0.

6. x = a is a graph of straight line parallel to y-axis and standard form of this equation is x + 0.y = a

7. y = b is a graph of straight line parallel to x-axis and standard form of this equation is 0.x + y = b.

8. The equation y = mx is always passing through the origin (0, 0).


Learn the steps for graphing linear equation in two variables:

1. Draw the graph of the linear equation y = 2x.

Solution:            

The given linear equation y = 2x is already in the form of y = mx + b [here b = 0]. 

Now we will apply the trial and error method to find 3 pairs of values of (x, y) which satisfy the given equation y = 2x.

When the value of x = 0, then y = 2 × 0 = 0

When the value of x = 1, then y = 2 × 1 = 2

When the value of x = 3, then y = 2 × 3 = 6

When the value of x = -1, then y = 2 × -1 = -2

When the value of x = -2, then y = 2 × -2 = -4

Arrange the values of the linear equation y = 2x in the table.

Linear Equation Table

Now, plot the points P (0, 0), Q (1, 2), R (2, 4), S (3, 6), T (-1, -2), U (-2, -4) on the graph paper.

Graph of Linear Equation

Join the points of P, Q, R, S, T and U.

We get a straight line passing through origin. This straight line is the graph of the equation y = 2x.

2. Draw the graph of the equation 4x - y = 3.

Solution:            

The given linear equation 4x - y = 3.

Now convert the given equation in the form of y = mx + b

4x - y = 3

⇒ 4x - 4x - y = - 4x + 3

⇒ - y = - 4x + 3

⇒ y = 4x - 3

Now we will apply the trial and error method to find 3 pairs of values of (x, y) which satisfy the given equation y = 4x - 3.

When the value of x = 0, then y = (4 × 0) - 3 = - 3

When the value of x = 1, then y = (4 × 1) - 3 = 1

When the value of x = 2, then y = (4 × 2) - 3 = 5

Arrange these value of the linear equation y = 4x - 3 in the table.

Equation Table

Now, plot the point P (0, -3), Q (1, 1), R(2, 5) on the graph.

Graphing Linear Equation

Join the points of P, Q and R.

We get a straight line passing through origin. This straight line is the graph of linear equation 4x - y = 3.

Related Concepts:

Coordinate Graph

Ordered pair of a Coordinate System

Plot Ordered Pairs

Coordinates of a Point

All Four Quadrants

Signs of Coordinates

Find the Coordinates of a Point

Coordinates of a Point in a Plane

Plot Points on Co-ordinate Graph

Graph of Linear Equation

Simultaneous Equations Graphically

Graphs of Simple Function

Graph of Perimeter vs. Length of the Side of a Square

Graph of Area vs. Side of a Square

Graph of Simple Interest vs. Number of Years

Graph of Distance vs. Time







7th Grade Math Problems

8th Grade Math Practice

From Graph of Linear Equation to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Converting Fractions to Decimals | Solved Examples | Free Worksheet

    Apr 28, 25 01:43 AM

    Converting Fractions to Decimals
    In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:

    Read More

  2. Expanded Form of a Number | Writing Numbers in Expanded Form | Values

    Apr 27, 25 10:13 AM

    Expanded Form of a Number
    We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its…

    Read More

  3. Converting Decimals to Fractions | Solved Examples | Free Worksheet

    Apr 26, 25 04:56 PM

    Converting Decimals to Fractions
    In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th…

    Read More

  4. Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

    Apr 26, 25 03:48 PM

    Worksheet on Decimal Numbers
    Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

    Read More

  5. Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table

    Apr 26, 25 01:00 PM

    Multiplication Table of Four
    Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times

    Read More