First slide

Equation of line in Straight lines

Question

If each of the points $(x_{1}, 4)$ and $(- 2, y_{1})$ lies on the line joining the points $(2, - 1)$ and $(5, - 3),$ then the point $P (x_{1}, y_{1})$ lies on the line

Moderate

A

$x = 3 y$
B

$x = - 3 y$
C

$y = 2 x + 1$
D

$2 x + 6 y + 1 = 0$

Solution

The equation of the line joining $(2, - 1)$ and $(5, - 3)$ is
$2 x + 3 y = 1$
Since $(x_{1}, 4)$ and $(- 2, y_{1})$ lie on $2 x + 3 y = 1 .$
$x_{1} = - 11 / 2$ and $y_{1} = 5 / 3$
Clearly, $P (x_{1}, y_{1}) = P (- 11 / 2, 5 / 3)$ lies on $2 x + 6 y + 1 = 0$ .

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