A coordinate plane is the rectangular plane formed with two number lines: one is vertical number line and the other one is the horizontal number line. In the horizontal number line, at left side, negative numbers are placed and at the right hand side, the positive numbers are placed. |

Figure of coordinate plane is shown below:

In the above figure, we can see that there are four quadrants and two axes. x - axis is plotted along horizontal line and y - axis is plotted along vertical line. As we know that in first quadrant, value of all Trigonometric Functions is positive. In case of second quadrant, only sin function is positive, rest all are negative. In third quadrant, tan function is positive and rest of the values is negative. In last or fourth quadrant, cos is positive and the rest are negative. In coordinate plane, positive values are plotted along right and upper side of origin and negative values are plotted along left side and lower side of origin point. This is all about the history of coordinate plane.

Coordinate plane is a two-dimensional plane surface on which points are plotted and located in x an y coordinates. It is a two dimensional plane surface, on which we cannot only plot points, but also lines and curves. There are two scales, x axis and y axis at the right angles. Two numbers - the x and y are used to locate the points on the plane, forming the horizontal and the vertical distances of the point from a particular location called the origin. Given below are some solved examples which will give you the right idea on how to graph coordinate plane.

### Solved Examples

**Question 1:**For a given equation, plot x and y coordinate plane, y = 3x + 7

**Solution:**

So, let us find out the ordered pairs

So, substitute x = 1, 2, 3, 4, 5

When x = 1, we get

y = 3 + 7

y = 10

When x = 2

y = 3 (2) + 7

y = 13

When x = 3

y = 3(3) + 7

y = 16

When x = 4

y = 3(4) + 7

y = 19

When x = 5

y = 3(5) + 7

y = 22

The order pairs of the given equation are

(1, 10), (2, 13), (3, 16), (4, 19), (5, 22)

**Question 2:**Plot a graph for the given equation y = 2x + 1

**Solution:**

First, let us calculate the x and y values. So, let us find out the ordered pairs.

So, substitute x = 1, 2, 3, 4, 5

When x = 1, we get

y = 2 + 1

y = 3

When x = 2

y = 2 (2) + 1

y = 5

When x = 3

y = 2 (3) + 1

y = 7

When x = 4

y = 2 (4) + 1

y = 9

When x = 5

y = 2 (5) + 1

y = 11

The order pairs of the given equation are

(1, 3), (2, 5), (3, 7), (4, 9), (5, 11)

**Question 3:**Plot a graph for the given equation y = 4x - 1

**Solution:**

First, let us calculate the x and y values. So, let us find out the ordered pairs

So, substitute x = 1, 2, 3, 4, 5

When x = 1, we get

y = 4 - 1

y = 3

When x = 2

y = 4 (2) - 1

y = 7

When x = 3

y = 4 (3) - 1

y = 11

When x = 4

y = 4 (4) - 1

y = 15

When x = 5

y = 4 (5) - 1

y = 19

The order pairs of the given equation are

(1, 3), (2, 7), (3, 11), (4, 15), (5, 19)