Question

Two points of a line are given below. The equation of the line is:

$E(-2,-3),F(-4,7)$

• A. $5x-y+7=0$
• B. $5x-y+13=0$
• C. $5x+y-7=0$
• D. $5x+y+13=0$

Answer 1

Answer: (D)

$5x+y+13=0$

The equation of a line $RT$ passing through the points $R(x_1,y_1)$ and $T(x_2,y_2)$ is

$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}$
For the given points: $E(-2,-3)$ and $F(-4,7)$
$\Rightarrow \frac{x+2}{-4+2}=\frac{y+3}{7+3}$
$\Rightarrow 10(x+2)=-2(y+3)$
$\Rightarrow 10x+20=-2y-6$
$\Rightarrow 10x+2y+26=0$
$\Rightarrow 5x+y+13=0$