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)
Explanation:
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:
$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left(x-x_{1}\right)$
Putting the values, we get
$y-(-3)=\frac{-5-(-3)}{4-2}(x-2)$
$\Rightarrow y+3=\frac{-5+3}{2}(x-2)$
$\Rightarrow y+3=\frac{-2}{2}(x-2)$
$\Rightarrow y+3=-1(x-2)$
$\Rightarrow y+3=-x+2$
$\Rightarrow x+y=2-3$
$\Rightarrow x+y=-1$
$\Rightarrow \frac{x}{-1}+\frac{y}{-1}=1$ (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)