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  • If the line x divided a plus y divided b is equal to 1 passes through the points 2, minus 3 and 4, minus 5 , then a, b is A. 1, 1 B. minus 1, 1 C. 1, minus 1 D. minus 1, minus 1

If the line \frac{x}{a}+\frac{y}{b}=1 passes through the points (2, –3) and (4, –5), then (a, b) is
A. (1, 1)
B. (– 1, 1)
C. (1, – 1)
D. (– 1, –1)

Answers (1)

The given points are (2, -3) and (4, -5) 

Firstly, the equation of line is found  

We know that the equation of line when two points are given is y-y1= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left ( x-x_{1} \right )

 Putting the values we get y-\left ( -3 \right )=\frac{-5-\left ( -3 \right )}{4-2}\left ( x-2 \right )

y+3=\frac{-5+3 }{2}\left ( x-2 \right )

 y+3=-\frac{2 }{2}\left ( x-2 \right )

 y+3= -1( x-2)  

 y+3= -x+2 

  x+y=2-3  

 x+y=-1  

\frac{x}{-1}+\frac{y}{-1}=1  in intercept form 

Comparing the equation with intercept form of the equation, that is \frac{x}{a}+\frac{y}{b}=1

the values of a = -1 and b = -1 

Hence, the correct option is (d)

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