Question

Which of the following is an equation of a line perpendicular to the line with equation $3x-6y=9$?

• A. $y=2$
• B. $3x+6y=9$
• C. $x-2y=3$
• D. $2x+y=3$
• E. $2x+2y=6$

Answer 1

The correct option is D $2x+y=3$

Given line is $3x-6y=9$
Dividing by $3$, we get

$x-2y=3$
Slope of the line $ax+by=c$ is given by $=-\frac{a}{b}$
So, slope of the given line $=\frac{1}{-2}=\frac{1}{2}$
Slope of the line perpendicular to a lien of slope $m$ is given by $=-\frac{1}{m}$
Hence, slope of the line, perpendicular to the given line will be $-2$
The equation of a line with slope $m$ is given as $y=mx+c$
Hence, required equation of perpendicular line will be $y=-2x+c$ OR $2x+y=c$
Where '$c$' can be any number.
Thus, Option $D$ is the correct answer.