Question

What is the equation of a line that passes through (0,1) and is perpendicular to the line $2x+y=1$?

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

Answer 1

The correct option is C $y=\frac{1}{2}x+1$

We are given with the equation of the line: $2x+y=1$.

Converting this equation to Slope-intercept form of the line: $y=mx+b$ where '$m$' is the slope of the line and '$b$' is the $y-$intercept of the line.

$y=-2x+1$
Slope of the above line is '-2' and $y-$intercept is '1'.

We need to find a perpendicular line to the above line.

Slope of line perpendicular to the above line$=m=\frac{-1}{-2}$
$m=\frac{1}{2}$
Also, line perpendicular to the above line passes through (0,1), this means that its $y-$intercept is '1'.

Equation of the line perpendicular to the line $2x+y=1$ is:
$y=mx+b$ where $m=\frac{1}{2}$ and $b=1$.

$y=\frac{1}{2}x+1$