Question

The equation of the line, which passes through $(2,7)$ and whose $y-$ intercept is $3$ is

• A. $2x-y-3=0$
• B. $2x-y+3=0$
• C. $2x+y-3=0$
• D. $2x+y+-3=0$

Answer 1

Answer: (B)

$2x-y+3=0$

Let the equation of the line be $\frac{x}{a}+\frac{y}{b}=1$ ..........(i)

when $a$ and $b$ are the $x$ and $y$ intercepts on the axes respectively.

The line passes through $(2,7)$ and $b=3$ ....(given).

Substituting $x=2$, $y=7$, $b=3$ in equation (i), we have

$\frac{2}{a}+\frac{7}{3}=1$

$\Rightarrow a=-\frac{3}{2}$

On putting $a=-\frac{3}{2}$ and $b=3$ in equation (i), we get

$\frac{x}{-\frac{3}{2}}+\frac{y}{3}=1$

$\Rightarrow 2x-y+3=0$