Question

A line $PQ$ passes through points $(3,-6)$ and $(-7,-4)$. Which of the following represents line parallel to $PQ$?

• A. $x+5y=6$
• B. $x+\frac{y}{2}=7$
• C. $y-2x=-9$
• D. $2y-x=-8$

Answer 1

The correct option is A $x+5y=6$

The slope of line $PQ$ passes through point $(3,-6)$ and $(-7,-4)$ is

$m=\frac{y_2-y_1}{x_2-x_1}$

$\Rightarrow m=\frac{-4-(-6)}{-7-3}$

$\Rightarrow m=\frac{-4+6}{-7-3}$

$\Rightarrow m=\frac{2}{-10}$

$\Rightarrow m=-\frac{1}{5}$

Use the point slope formula with one of point $(3,-6)$ and slope $-\frac{1}{5}$

$y-(-6)=-\frac{1}{5}(x-3)$

$\Rightarrow 5(y+6)=-x+3$

$\Rightarrow 5y+30+x-3=0$

$\Rightarrow x+5y+27=0$

Then line parallel to $PQ$ is same slope $-\frac{1}{5}$

Then line $x+5y=6$

$x+5y=6$

$\Rightarrow 5y=-x+6$

$\Rightarrow y=-\frac{1}{5}x+\frac{6}{5}$ is same solpe is $-\frac{1}{5}$

Then answer is (A)