## Note on Equation of a Straight Line

• Note
• Things to remember
• Videos
• Exercise
• Quiz

#### Straight Line

The equation of the straight line can be calculated in different ways according to the given condition. The different conditions of equation of straight line are given below:

#### Horizontal, Vertical and Oblique lines

1. The equation of the straight line parallel to X-axis: Equation of the straight line parallel to X-axis and passing through the point (o, b) cutting at Y-axis i.e. at y = b.
2. The equation of the straight line parallel to Y-axis: Equation of the straight line parallel to Y-axis and passing through the point (a, O) cutting at X-axis is x=a.
3. The oblique line: A line which is neither parallel to x-axis nor parallel to they-axis is called an oblique line.

#### Inclination of a line

When the angle is made in a straight line with x-axis making positive direction is said to be the inclination of a line. It is devoted by θ.

#### Slope of Straight line

The tangent of the angle made by the straight line on the positive X-axis is called slope of the straight line. It is denoted by m. If θ be the angle made by the straight line AB on X-axis, then slope AB = m = tanθ

#### Collinear Point

If three or more than three points lies in same straight line then it is said to be collinear points. We can prove the point P, Q, and R collinear by using slope as a slope of PQ = slope of QR =` slope of PR. As the points P, Q, and R in collinear. If the points P, Q, and R lie on the same line the slope of the two line will equal.

#### Intercepts made by a line on the axis

If the line AB cuts the X and Y - axis at the points A (a, O) and B(0, b) respectively. Then the length from the origin to the point of intersection of the line AB and X - axis is called the x -intercept and length from the point of intersection of the line AB and Y - axis are called y - intercept. In the figure , x -intercept OA = a and y -intercept OB = b.

Convention for the signs of intercepts

• If the X-intercepts is measured in right side from the origin then it is considered as positive and measured on the left side from the origin then it is considered as negative.
• If the Y-intercept is measured over the origin then it is considered as positive and measured on the under the origin then it is considered as negative.

#### Equation of a straight line parallel to X-axis

Let AB be a straight line parallel to X-axis. Then the ordinate of every point on the line XY is constant say b.
Let P(x, y) be any point on the lie AB. From P, draw PM perpendicular to X-axis, then MP = y.
∴ y = b, which is required equation of the line AB. The line AB. The line y = b lies above or below the X-axis according to as b is positive or negative.
If b = 0, then the line Ab coincides with X-axis. So, the equation of X-axis is y = 0.

#### Equation of straight line parallel to Y-axis

Let AB be a straight line parallel to Y-axis. Then, the abscissa of every point on the line AB is constant, say a.
Let P(x, y) be any point on the AB. From P, draw PN perpendicular to Y-axis, then NP = x.
∴ x = a, which is required equation of the line AB. The line x = a lies to the right or left of Y-axis according to as a is positive or negative.
If a = 0, then the line Ab coincides with y-axis.

The equation of the straight line in the standard form: There are three standard forms of the equation of the straight line.They are:
Slope - intercept form: If the slope of the straight line m = tanθ and y - intercept (c) are known, the equation of the straight line in slope-intercept form is y = mx + c.

1. If the straight line passes through the origin then y - intercept of c = 0. In this case, an equation of the straight line is y = mx.
2. The tangent of the angle made by the straight line on the positive X-axis is called slope of the straight line.
3. When the angle is made in a straight line with x-axis making positive direction is said to be the inclination of a line. It is devoted by θ.
4. If three or more than three points lies in same straight line then it is said to be collinear points.
.

### Very Short Questions

Here, given points (2,5)

The equation of the straight line parallel to y-axis is x=x coordinatesof given points

or, x=2

∴x-2=0Ans.

Here,

given points (5,-2)

The equation of the straight line parallel to y-axis is x=x coordinatesof given points

or, x=5

∴x-5=0Ans.

Given points,(-3,2)

The equation of the straight line parallel to x-axis is y=y-coordinates of the point.

or, y=2

∴ y-2=0.Ans.

Given points,(-3,2)

The equation of the straight line parallel to x-axis is y=y-coordinates of the point.

or, y=-4

∴ y+4=0.Ans.

Here,

The equation of the straight line parallel to x-axis and 4 units above the origin is y=4 and 4 units below the origin is y=-4.

∴The required equation are y-4=0 and y+4=0.Ans.

Here,

Angle on x-axis (θ)=45° and slope of the line(m)=tan 45θ°=1

Equation of straight line passing through origin is y=mx.

or, y=1,x

∴y-x=0.Ans.

Angle on x-axis (θ)=150°

∴ Slope (m)=tanθ=tan150°=-$$\frac{1}{√3}$$

Using formula,y=mx

y=-$$\frac{1}{√3}$$x

or,√3y=-x

∴x+√3y=0.Ans.

Here,

Given equation,x-y=5

or, -y=-x+5...........(i)

Comparing equation (i) with y = mx+c, we get

m=1 and c=-5

∴Slope (m)=1 and y-intercept (c)=-5.Ans.

Here given equation, y=√3 x or y=√3 x+0........(i)

Comparing equation (i) with y=mx +c,we get,

Slope (m)=√3 and y-intercept(c)=0 Ans.

0%

12

8

3

21

4

10

9

2

12/5

11/5

17/6

17/5

x=-10

x=-19

x=10

x=-18

k=10

k=1

k=2

k=-9

3x-y=2

5x+y=4

3x-y=9

3x+y=4

y=2x+1

y=3x+7

y=3x+1

y=3x-1

2x+5y=26

2x-9y=21

2x+4y=26

2x-5y=12

x√2-y=3-4√2

x√3-y=3-4√3

x√3-y=3+4√3

x√3-y=2-2√3

x-y-1=0
x+y+1=0
x-y+4=0
x-y+2=0

## DISCUSSIONS ABOUT THIS NOTE

You must login to reply

Forum Time Replies Report
##### Aiyaan

Find the equation of the line joining the origin and the points of trisection of join of (1,4) and (2,3).

You must login to reply

##### Popular Chaube

How to find out the equation of a straight line having equation and a point on X axis?

You must login to reply