Equation of a line passing through two points

Question:Find the equation of the line passing through the points (9,7) and (5,2).

Solution:
Step1: Put the difference of the y - coordinates as the x - coefficient and vice -versa.
i.e. x coefficient = 7 - 2 = 5
y coefficient = 9 - 5 = 4.
Thus L.H.S of equation is 5x - 4y.


Step 2: The constant term (R.H.S) is obtained by substituting the co-ordinates of either of the given points in
L.H.S (obtained through step-1)
i.e. R.H.S of the equation is

5(9) - 4(7) = 45 - 28 = 17
or 5(5) - 4(2) = 25 - 8 = 17.


Thus the equation is 5x - 4y = 17.


Example: Find the equation of the line passing through (2, -3) and (4,-7).

Step 1 : x[-3-(-7)] –y[2-4] = 4x + 2y.
Step 2 : 4(2) + 2(-3) = 8 –6 = 2.
Step 3 : Equation is 4x + 2y =2 or 2x +y = 1.