FIND THE EQUATION OF THE LINE FROM THE GIVEN POINT AND SLOPE EXAMPLES

In this section, you will learn how to find the equation of a line from the given point and slope.

Equation of the line using the slope and a point on the line : 

(y - y₁)  =  m(x - x₁)

Here, we have to consider the given point as (x₁, y₁) and slope as 'm'.

Example 1 :

Find the equation of a straight line whose slope is 7 and which passes through the point (5,-6).

Solution :

Slope (m) = 7 and the point (x₁,y₁) = (5,-6)

(y - y₁)  =  m(x - x₁)

(y - (-6))  =  7 (x - 5)

(y + 6)  =  7 (x - 5)

y + 6  =  7x - 35

7x + y + 35 + 6  =  0

7x + y + 41  =  0

Example 2 :

Find the equation of a straight line whose slope is 6 and which passes through the point (-1, -2) 

Solution :

Slope (m) = 6 and the point (x₁,y₁) = (-1,-2)

(y - y₁) = m (x - x₁)

(y - (-2))  =  6(x-(-1))

(y + 2)  =  6(x + 1)

y + 2  =  6x + 6

6x - y + 6 - 2  =  0

6x - y + 4  =  0

Example 3 :

Find the equation of a straight line whose slope is 2/3 and which passes through the point (-2,-4) 

Solution :

Slope (m)  =  2/3 and the point (x₁,y₁)  =   (-2,-4)

(y - y₁)  =  m (x - x₁)

(y -  (-4))  =  (2/3) (x - (-2))

(y + 4)  =  (2/3) (x + 2)

3(y + 4)  =  2(x + 2)

3y - 12  =  2 x + 4

2x - 3 y + 4 + 12  = 0

2x - 3 y + 16  = 0

Example 4 :

Find the equation of a straight line whose slope is -1/5 and which passes through the point (-3,-1) 

Solution :

Slope (m) = -1/5 and the point (x₁,y₁) = (-3,-1)

Equation of a line:

(y - y₁)  =  m (x - x₁)

(y - (-1))  =  (-1/5) (x - (-3))

 (y + 1)  =   (-1/5) (x + 3)

5 (y + 1)  = -1 (x + 3)

5 y + 5 = - 1 x - 3

x + 5 y + 3 + 5 = 0

x + 5 y + 8 = 0

Example 5 :

Find the equation of a straight line whose slope is -2/7 and which passes through the point (-5,-4) 

Solution :

Slope (m) = -2/7 and the point (x₁,y₁) = (-5,-4)

(y - y₁)  =  m (x - x₁)

(y - (-4))  =  (-2/7) (x - (-5))

(y + 4)  =   (-2/7) (x + 5)

7 (y + 4)  =  -2 (x + 5)

7 y + 28  =  - 2 x - 10

2 x + 7 y + 28 + 10  =  0

2 x + 7 y + 38  =  0

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