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'.
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
Example 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
Example 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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