Example 1 :
Find the equation of the line which is passing through the points (1, 4) and (3, -2).
Solution :
Here (x_{1}, y_{1}) = (1, 4) and (x_{2}, y_{2}) = (3, -2).
Equation of a line :
(y - y_{1})/(y_{2 }- y_{1}) = (x - x_{1})/(x_{2 }- x_{1})
(y - 4)/(-2 - 4) = (x - 1)/(3 - 1)
(y - 4)/(-6) = (x - 1)/2
2(y - 4) = (x - 1)(-6)
2y - 8 = - 6 x + 6
6x + 2y - 8 - 6 = 0
6x + 2y - 14 = 0
Dividing the entire equation by 2,
3x + y - 7 = 0
Example 2 :
Find the equation of the line which is passing through the points (0, 4) and (3, 1).
Solution :
Here (x_{1}, y_{1}) = (0, 4) and (x_{2}, y_{2}) = (3, 1).
Equation of a line :
(y - 4)/(1 - 4) = (x - 0)/(3 - 0)
(y - 4)/(-3) = x/3
3(y - 4) = x(-3)
3y - 12 = - 3 x
3x + 3y - 12 = 0
÷ by 3 => x + y - 4 = 0
Example 3 :
Find the equation of the line which is passing through the points (3, 1) and (-3, 2).
Solution :
Here (x_{1}, y_{1}) = (3, 1) and (x_{2}, y_{2}) = (-3, 2).
Equation of a line :
(y - 1)/(2 - 1) = (x - 3)/(-3 - 3)
(y - 1)/1 = (x - 3)/(-6)
(-6)(y - 1) = 1(x - 3)
-6y + 6 = x - 3
x + 6y - 3 - 6 = 0
x + 6y - 9 = 0
Example 4 :
Find the equation of the line which is passing through the points (2, 6) and (1, 2).
Solution :
Here (x_{1}, y_{1}) = (2, 6) and (x_{2}, y_{2}) = (1, 2).
Equation of a line:
(y - 6)/(2 - 6) = (x - 2)/(1 - 2)
(y - 6)/(-4) = (x - 2)/(-1)
(-1)(y - 6) = (-4)(x - 2)
-y + 6 = -4x + 8
4x - y + 6 - 8 = 0
4x - y - 2 = 0
Example 5 :
Find the equation of the line which is passing through the points (5, -5) and (2, 7)
Solution :
Here (x_{1}, y_{1}) = (5, -5) and (x_{2}, y_{2}) = (2, 7).
Equation of a line :
(y - (-5))/(7 - (-5)) = (x - 5)/(2 - 5)
(y + 5)/(7 + 5) = (x - 5)/(-3)
(y + 5)/12 = (x - 5)/(-3)
-3(y + 5) = 12(x - 5)
-3y - 15 = 12 x - 60
12 x + 3y - 60 + 15 = 0
12 x + 3y - 45 = 0
÷ by 3 => 4 x + y - 15 = 0
Example 6 :
Find the equation of the line which is passing through the points (1, 3) and (0, 7).
Solution :
Here (x_{1}, y_{1}) = (1, 3) and (x_{2}, y_{2}) = (0, 7).
Equation of a line :
(y - 3)/(7 - 3) = (x - 1)/(0 - 1)
(y - 3)/4 = (x - 1)/(-1)
-1(y - 3) = 4(x - 1)
-y + 3 = 4 x - 4
4 x + y - 4 - 3 = 0
4 x + y - 7 = 0
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