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