EQUATION OF LINE IN THE XY PLANE WITH SLOPE AND CONTAINING THE POINT

Equation of the line containing the point and slope :

(y - y1)  =  m(x - x1)

Equation of the line containing two points :

(y - y1)/(y2 - y1)  =  (x - x1)/(x - x1)

Example 1 :

Find the equation of the line in the xy-plane with slope −4 that contains the point (−5,−2).

Solution :

(y - y1)  =  m(x - x1)

(x1, y1)  ==>  (-5, -2) and m  =  -4

(y - (-2))  =  -4(x - (-5))

(y + 2)  =  -4(x + 5)

y + 2  =  -4x - 20

4x + y + 2 + 20  =  0

4x + y + 22  =  0

Example 2 :

Find the equation of the line that contains the points (2,−1) and (4, 9).

Solution :

(y - y1)/(y2 - y1)  =  (x - x1)/(x - x1)

(y + 1)/(9 + 1)  =  (x - 2)/(4 - 2)

(y + 1)/10  =  (x - 2)/2

2(y + 1)  =  10(x - 2)

2y + 2  =  10x - 20

10x - 2y - 20 - 2  =  0

10x - 2y - 22  =  0 

5x - y - 11  =  0

Example 3 :

Find the equation of the line that contains the points (−3, 2) and (−5, 7).

Solution :

(y - y1)/(y2 - y1)  =  (x - x1)/(x - x1)

(y - 2)/(7 - 2)  =  (x + 3)/(-5 + 3)

(y - 2)/5  =  (x + 3)/(-2)

-2(y - 2)  =  5(x + 3)

-2y + 4  =  5x + 15

5x + 2y + 15 - 4  =  0

5x + 2y + 11  =  0

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