Find the equation passing through the two points 2 1 and 5 2

Find the equation passing through the two points (-2, 1) and (5, 2)

Solution

Let the equation of the required line be y = mx +c. Since this line passes through the points ( -2 , 1) and ( 5, 2) , on substituting these values of x and y in the equation of the line, we have:

1 = m ( - 2) + c or, c = 2m +1....(1) and

2 = m (5) + c or, c = - 5m + 2 ....(2) . On equating the two values of c from the 1st and the 2nd equations, we have

2m + 1 = - 5m + 2. Therefore, 7m = 2 -1 = 1 or, m = 1/7 . On substituting this value of m in the 1stequation, we get

c = 2m + 1 = 2/7 + 1 = 9/7. Thus the equation of the required line is y = x/7 + 9/7