Coordinate plane has a rectangular axes where the horizontal line represent the x values and vertical lines represent the y values. We can work out two concurrent equations in x and y by representation of graphs corresponding to the equations. An equation in x and y is in the form ofÂ $a x + b y + c = 0$. The equation correspond to a straight line, so, the problem of solving two concurrent equations in x and y decreases to the problem of finding the familiar point stuck between the two corresponding lines. To graph an equation on the coordinate plane we need a set of coordinates falling on the curve of the given equation. Joining the dots the curve can be completed.

**Following steps are used for graphing coordinate plane:**

** **In graphing, to plot graph on a plane. Basically, we need two axes as x-axis and y-axis compulsory.

In a plane x-axis value is zero for y, in y-axis x value is zero.

The given steps are used to plot the graph for a line equation in a plane.

**Step 1:**** **Put few different values of x in the equation y = f(x) and get the corresponding values of y. Hence, different (x, y) values are obtained. Also, find the value of y at x = 0, and value of x at y = 0 to obtain the intercepts.

**Step 2: **Draw coordinate plane and mark the points on both the axes on equal intervals.

**Step 3: **Plot the obtained coordinate points on the plane drawn.

**Step 4:**Join the points to graph the curve.

Examples to graphing on a coordinate plane are as follows:

**Example 1: **

**Solution:**Substituting *x **= -1, 0.5, 1, 2* in the equation of the line, we get y = -7, -4, -3, -1 equivalently. In a graph, plot the

Points *(-1, -7), (0.5, -4), (1, -3), (2, -1) *

X |
0.5 | 1 | 2 |

Y |
-4 | -3 |
-1 |

Link the points by a line fragment and lengthen it in each direction. Thus we obtain the linear graph solution.

**Example 2: **Draw the graph of the line** ***2x + y = 7.*

**Solution: **The given equation is rewritten as *y = 7 - 2x. *

Substituting *x = -1* then y* = *7 - (-2) = 9.

*x = *0, then* *y* = *7

*x = 2** *then y *= *7 - 4 = 3.

Plot x and y values in the graph sheet. *[(-1, 9), (0, 7)* and *(1, 3)]*

** **

X |
-1 | 0 | 2 |

Y |
9 |
7 |
3 |

Link the points by a line fragment and expand it in both the ways. Thus we obtain the linear graph solution.

**1. **Draw the graph of the following: *y = 3x - 1*

** ****Answer: **

X | -1 | 0 | 1 |

Y | -4 | -1 | 1 |

**2. **Draw the graph of the line equations: *3y + 2x - 12 = 0.*

** ****Answer:**** **

X | -1 | 0 | 1 |

Y | 5.5 | 4 | 2.5 |

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