**Graphing linear equations in two variables examples :**

**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.

Let us look into the next example on "Graphing linear equations in two variables examples"

**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.

**Let us look into the next example on "Graphing linear equations in two variables examples"**

**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, "Graphing linear equations in two variables examples".

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