# Choose the correct answer from the given four options. If the line $\large\frac{x}{a}$$+ \large\frac{y}{b}$$=1$ passes through the points (2, –3) and (4, –5), then (a, b ) is

$\begin {array} {1 1} (A)\;(1, 1) & \quad (B)\;(-1,1) \\ (C)\;(1,-1) & \quad (D)\;(-1,-1) \end {array}$

Toolbox:
• If a line $ax+by+c=0$ passes through a point $(x_1, y_1)$, then the coordinates can be substituted in the place of $x$ and $y$.
Step 1:
Given equation of the line is
$\large\frac{x}{a}$$+\large\frac{y}{b}$$=1$
$\Rightarrow bx+ay=ab$
It is given that this line passes through (2, -3)
$\therefore b(2)+a(-3)=ab$
(i.e) $2b-3a=ab$--------(1)
It also passes through (4, -5)
$\therefore 4b-5a=ab$--------(2)
On solving equation (1) and (2)
$(\times 2 ) 2b-3a=ab$
$\qquad 4b-5a=ab$
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$\qquad 4b-6a=2ab$
$\qquad 4b-5a=ab$
$\quad (-) \quad (+) \quad (-)$
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$\quad \qquad -a = ab$
$\therefore b = -1$
and substituting for $b$ in equation (1) we get,
$2(-1)-3a=ab$
$-2-3a=a(-1)$
$-3a+a=2$