First slide

Equation of line in Straight lines

Question

The point $P (a, b)$ lies on the straight line $3 x + 2 y = 13$ and the point $Q (b, a)$ lies on the straight line $4 x - y = 51$ then the equation of the line $P Q$ is

Moderate

A

$x - y = 5$
B

$x + y = 5$
C

$x + y = - 5$
D

$x - y = - 5$

Solution

It is given that points $P (a, b)$ and $Q (b, a)$ lie on the lines $3 x + 2 y = 13$ and $4 x - y = 5$ respectively.
$∴ 3 a + 2 b = 13$ and $4 b - a = 5 \Rightarrow a = 3, b = 2$
Thus, the coordinates of $P$ and $Q$ are $(3, 2)$ and $(2, 3)$ respectively. So, the equation of line $P Q$ is
$y - 2 = \frac{3 - 2}{2 - 3} (x - 3)$ or, $x + y = 5$

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