Question

Find the equation of a line through the given pair of point `(2,2/3)` and `((-1)/2, -2)`

Answer 1

Equation of the line passing through the point `(2, 2/3)` and `((-1)/2, -2)`

`(y - y_1)/(y_2 - y_1) = (x - x_1)/(x_2 - x_1)`

`(y - 2/3)/(-2 - 2/3) = (x - 2)/(-1/2 - 2)`

⇒ `((3y - 2)/3)/((-6 - 2)/3) = ((x - 2)/(-1 - 4))/2`

`(3y - 2)/3 xx 3/(-8) = (x - 2)/((-5)/2)`

⇒ `(3y -2)/(-8) = (2(x - 2))/(-5)`

– 5(3y – 2) = – 8 × 2 (x – 2)

– 15y + 10= – 16 (x – 2)

– 15y + 10= – 16x + 32

16x – 15y + 10 – 32 = 0

16x – 15y – 22 = 0

The required equation is 16x – 15y – 22 = 0