**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

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.

**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

x y |
-1 -6 |
0 0 |
1 6 |

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).

x y |
5 -2 |
5 0 |
5 2 |

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)x y = (-5/3) x + 2 |
-3 5 7 |
0 0 2 |
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

x 4x y = 4x-1 |
-1 -4 -5 |
0 0 -1 |
1 4 3 |

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)x y = (-2/3)x + 4 |
-3 2 6 |
0 0 4 |
3 -2 2 |

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".

Apart from the stuff given above, if you want to know more about "Graph linear equations", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**