Question

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

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

Answer 1

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

Slope of the line perpendicular to $y=-2x+3$ is $m=\frac{-1}{(-2)}=0.5$

(Since both are perpendicular product of both the slopes is $-1$).

$y$-intercept of the line $y=2x-3$ is $-3$.

Now the equation of the line having slope as $\frac{1}{2}$ and $y$-intercept as $-3$ is $y=0.5x+(-3)$.

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