HOW TO FIND THE EQUATION OF THE LINE FROM THE GIVEN POINT AND SLOPE

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 slope point form :

(y - y1)  =  m(x - x1)

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

Examples

Example 1 :

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

Solution :

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

Equation of a line:

(y - y1)  =  m (x - x1)

(y - (-3))  =  5 (x - 1)

(y + 3)  =  5 (x - 1)

y + 3  =  5x - 5

5x - y - 5 - 3  =  0

5x - y - 8  =  0

Example 2 :

Find the equation of a straight line whose slope is -1/5 and which passes through the point (4, 8)

Solution :

Slope (m)  =  -1/5 and the point (x1, y1)  =  (4, 8)

(y - y₁)  =  m (x - x₁)

(y - 8)  =  (-1/5) (x - 4)

5 (y - 8)  =  -1(x - 4)

5y - 40  =  -1x + 4

x - 5 y - 40 - 4  =  0

x - 5 y - 44  =  0

Example 3 :

Find the equation of a straight line whose slope is 1/7 and which passes through the point (-1,8)

Solution :

Slope (m)  =  1/7 and the point (x1, y1) ==> (-1, 8)

(y - y1)  =  m (x - x1)

(y - 8)  =  (1/7)(x - (-1))

7(y - 8)  =  1 (x + 1)

7y - 56  =  1 x + 1

x - 7y + 56 + 1  =  0

x - 7y + 57  =  0 

Question 4 :

Find the equation of a straight line whose slope is 2/5 and which passes through the point (0,-7)

Solution :

Slope (m)  =  2/5 and the point (x1, y1)  =  (0, -7)

(y - y1)  =  m (x - x1)

(y - (-7))  =  (2/5)(x - 0)

(y + 7)  =  (2/5) (x)

5 (y + 7)  =  2x

5y + 35  =  2 x

2x - 5y - 35  =  0


Question 5 :

Find the equation of a straight line whose slope is 5/7 and which passes through the point (-2,-1)

Solution :

Slope (m)  =  5/7 and the point (x₁,y₁)  ==> (-2, -1)

(y - y1)  =  m (x - x1)

(y - (-1))  =  (5/7)(x - (-2))

(y + 1)  =  (5/7) (x + 2)

7 (y + 1)  =  5 (x + 2)

7 y + 7  =  5 x + 10

5 x - 7 y + 10 - 7  =  0

5 x - 7 y + 3  =  0

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