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 - y_{1}) = m(x - x_{1})
Here, we have to consider the given point as (x_{1}, y_{1}) 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 (x_{1}, y_{1}) = (5, -6).
Equation of the line :
(y - y_{1}) = m(x - x_{1})
(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 (x_{1}, y_{1}) = (-1,-2).
Equation of the line :
(y - y_{1}) = m(x - x_{1})
(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 (x_{1}, y_{1}) = (-2,-4).
Equation of the line :
(y - y_{1}) = m(x - x_{1})
(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 (x_{1}, y_{1}) = (-3,-1).
Equation of the line :
(y - y_{1}) = m(x - x_{1})
(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 (x_{1}, y_{1}) = (-5,-4).
Equation of the line :
(y - y_{1}) = m(x - x_{1})
(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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