In geometry, a coordinate plane is used for assigning a unique set of numbers. In 3 dimensions, coordinate system has mutually perpendicular axis that locate each of the 3 coordinates denoted as x, y and z.

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple.

(X, Y) is the general form of the coordinates.

The X coordinate is generally plotted on horizontal axis.

The Y coordinate is generally plotted on vertical axis.

Both of the X and Y values are points of the coordinates.

Here is a simple example, lets graph (3, 2) coordinate on a graph sheet.

Select 3 on the x axis & then 2 on the y axis. Now, select the point where both the points meet.

Thus you got the coordinate for the given values (3, 2).

Here are problems based on x and y coordinate:

### Solved Examples

**Question 1: **Graph the Equation 4x + y = 20

** Solution: **
We see that when

x = 1, 2, 3, 4

we have

Put x = 1

4(1) + y = 20

4 + y = 20

y = 20 - 4

y = 16

Put x = 2

4(2) + y = 20

8 + y = 20

y = 20 - 8

y = 12

Put x = 3

4(3) + y = 20

12 + y = 20

y = 20 - 12

y = 8

Put x = 4

4(4) + y = 20

16 + y = 20

y = 20 - 16

y = 4

In x y coordinates we have

(1, 16), (2, 12), (3, 8), and (4, 4)

The above graph forms a x y coordinates.

**Question 2: ****Consider the equation 5x + y = 40 and draw a graph of it.** ** Solution: **
We see that when

x = 2, 4, 6, 8

we have

Put x = 2

5(2) + y = 40

10 + y = 40

y = 40 - 10

y = 30

Put x = 4

5(4) + y = 40

20 + y = 40

y = 40 - 20

y = 20

Put x = 6

5(6) + y = 40

30 + y = 40

y = 40 - 30

y = 10

Put x = 8

5(8) + y = 40

40 + y = 40

y = 40 - 40

y = 0

In x y coordinates we have

(2, 15), (4, 20), (6, 10), and (8, 0)

The above graph forms a x y coordinates.

**Problem 1:** Graph the points (5, 6), (-8, 0) and (0, 2) on a coordinate plane.

**Problem 2:** The points (-2, -4), (9, 7) and (8, -8) will fall in which quadrants?