Let us consider a straight line pass which is passing through the two points (x_{1}, y_{1}) and (x_{2}, y_{2}) as shown below.
Example 1 :
Find the slope of the straight line passing through the points (3, - 2) and (-1, 4).
Solution :
Formula to find the slope of the line passing through two points is
m = (y_{2} - y_{1})/(x_{2 }- x_{1})
Substitute (x_{1}, y_{1}) = (3, -2) and (x_{2}, y_{2}) = (-1, 4).
m = [4 - (-2)]/(-1 - 3)
= (4 + 2)/(-4)
= 6/(-4)
= -3/2
So, the slope of the given line is -3/2.
Example 2 :
Find the slope of the straight line passing through the points (5, - 2) and (4, -1).
Solution :
Formula to find the slope of the line passing through two points is
m = (y_{2} - y_{1})/(x_{2 }- x_{1})
Substitute (x_{1}, y_{1}) = (5, -2) and (x_{2}, y_{2}) = (4, -1).
m = [-1 - (-2)]/(4 - 5)
= (-1 + 2)/(-1)
= 1/(-1)
= -1
So, the slope of the given line is -1.
Example 3 :
Find the slope of the straight line passing through the points (-2, - 1) and (4, 0).
Solution :
Formula to find the slope of the line passing through two points is
m = (y_{2} - y_{1})/(x_{2 }- x_{1})
Substitute (x_{1}, y_{1}) = (-2, -1) and (x_{2}, y_{2}) = (4, 0).
m = (0 - 1)/[4 - (-2)]
= -1/(4 + 2)
= -1/6
So, the slope of the given line is -1/6.
Example 4 :
Find the slope of the straight line passing through the points (1, 2) and (-4, 5).
Solution :
Formula to find the slope of the line passing through two points is
m = (y_{2} - y_{1})/(x_{2 }- x_{1})
Substitute (x_{1}, y_{1}) = (1, 2) and (x_{2}, y_{2}) = (-4, 5).
m = (5 - 2)/(-4 - 1)
= 3/(-5)
= -3/5
So, the slope of the given line is -3/5.
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