Question

Which of the following lines is perpendicular to $y=-3x+2$ and has the same $y$-intercept as $y=3x-2$?

• A. $y=-\frac{1}{3}x$
• B. $y=-\frac{1}{3}x+2$
• C. $y=-\frac{1}{3}x-2$
• D. $y=\frac{1}{3}x-2$
• E. $y=\frac{1}{3}x+2$

Answer 1

The correct option is D $y=\frac{1}{3}x-2$

The equation of given line $y=-3x+2$ is $-3$

Let the equation of line perpendicular to given line be $m$

Therefore we have $m\times (-3)=-1$

$\Rightarrow$ $m=\frac{1}{3}$

The $y$- intercept of given line $y=3x-2$ is $-2$

Therefore the equation of required line with slope $\frac{1}{3}$ and $y$-intercept $-2$ is

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