Prove the following


If the line $\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1$ passes through the points $(2,-3)$ and $(4,-5)$, then $(\mathrm{a}, \mathrm{b})$ is

A. (1, 1)

B. (– 1, 1)

C. (1, – 1)

D. (– 1, –1)


D. (– 1, –1)


Given points are $(2,-3)$ and $(4,-5)$ Firstly,

we find the equation of line.

We know that,

Equation of line when two points are given:


Putting the values, we get


$\Rightarrow y+3=\frac{-5+3}{2}(x-2)$

$\Rightarrow y+3=\frac{-2}{2}(x-2)$

$\Rightarrow y+3=-1(x-2)$

$\Rightarrow y+3=-x+2$

$\Rightarrow x+y=2-3$

$\Rightarrow x+y=-1$

$\Rightarrow \frac{x}{-1}+\frac{y}{-1}=1$ (Intercept form)

Comparing the above equation with the given equation $\frac{x}{a}+\frac{y}{b}=1$, we get the

value of $a$ and $b$

$a=-1$ and $b=-1$


Hence, the correct option is (d)



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