First slide

Equation of line in Straight lines

Question

Equations of the straight lines passing through the point $(4, 3)$ and making intercepts on the coordinate axes whose sum is $- 1$ are

Moderate

A

$x / 2 + y / 3 = 1$ and $x / 2 + y / 1 = 1$
B

$x / 2 - y / 3 = - 1$ and $x / (- 2) + y / 1 = - 1$
C

$x / 2 + y / 3 = 1$ and $x / (- 2) + y / 1 = - 1$
D

$x / 2 - y / 3 = 1$ and $x / (- 2) + y / 1 = 1$

Solution

Let the equation of the line be $\frac{x}{a} + \frac{y}{- 1 - a} = 1 .$
Since it passes through $(4, 3), \frac{4}{a} + \frac{3}{- 1 - a} = 1$
$\Rightarrow a^{2} = 4 \Rightarrow a = \pm 2$
and the required equations are
$\frac{x}{2} + \frac{y}{- 3} = 1$ and $\frac{x}{- 2} + \frac{y}{1} = 1$

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