# GRAPH LINEAR EQUATIONS

## About "Graph Linear Equations"

Graph Linear Equations :

The equation which is in the form ax + by + c = 0 is known as linear equation.

A first degree equation in two variables always represents a straight line. Hence we can take general equation of a straight line as ax + by + c = 0, with at least one of a or b not equal to zero.

The general equation of a straight line is ax + by + c = 0

(i) If c = 0, then the equation becomes ax + by = 0 and the line passes through the origin

(ii) If a = 0, then the equation becomes by + c = 0 and the line is parallel to x-axis

(iii) If b = 0, then the equation becomes ax + c = 0 and the line is parallel to y-axis

## Procedure to Draw a Linear Graph

When graphing an equation, we usually begin by creating a table of x and y values. We do this by choosing three x values and computing the corresponding y values. Although two points are sufficient to sketch the graph of a line, we usually choose three points so that we can check our work.

Step 1 : Using the given equation construct a table of with x and y values.

Step 2 : Draw x - axis and y - axis on the graph paper.

Step 3 : Select a suitable scale on the coordinate axes.

Step 4 : Plot the points

Step 5 : Join the points and extend it to get the line.

## Graph linear equations - Examples

Example 1 :

Draw the graph of y = 6x

Solution :

Substituting the values x = - 1, 0, 1 in the equation of the line, we find the values of y as follows

 xy -1-6 00 16

In a graph, plot the points (-1, -6), (0, 0) and (1, 6) and draw a line passing through the plotted points. This is the required linear graph.

Example 2 :

Draw the graph of x = 5

Solution :

The line x = 5 is parallel to y-axis. On this line x = 5, a constant. So, any point on this line is of the form (5, y). Taking the values y =- 2, 0, 2 we get the points (5, -2), (5, 0) and (5, 2).

 xy 5-2 50 52

In a graph sheet, plot these points and draw a line passing through the points. Thus we get the required linear graph.

Example 3 :

Draw the graph of the line y = (5/3)x + 2

Solution :

Substituting x = -3, 0, 3 in the equation of the line, we find the values of y as follows

 x(-5/3)xy = (-5/3) x + 2 -357 002 3-5-3

Plot the points (-3, 7), (0, 2) and (3, -3) and draw a line passing through the plotted points. This is the required graph of the equation y = (-5/3)x + 2

Example 4 :

Draw the graph of y = 4x - 1.

Solution :

Substituting the values x = - 1, 0, 1 in the given equation of line, we find the values of y as follows

 x4xy = 4x-1 -1-4-5 00-1 143

Plot the points (-1, -5), (0, -1) and (1, 3) in a graph sheet and draw a line passing through the plotted points. We now get the required linear graph.

Example 5 :

Draw the graph of 2x + 3y = 12

Solution :

First, we rewrite the equation 2x + 3y = 12 in the form of y=mx+c.

2x+3y = 12 implies y = (2/3)x + 4

Substituting x = - 3, 0, 3 in the above equation, we find the values of y as follows

 x(-2/3)xy = (-2/3)x + 4 -326 004 3-22

Plot the points (-3, 6), (0, 4) and (3, 2) and draw a line passing through these points. Now we get the required graph.

After having gone through the stuff given above, we hope that the students would have understood, "Graph linear equations".

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