Question

A line is passing through a point $(0,-\frac{1}{2})$. This line is perpendicular to the line having slope of 5. Find the equation of this line.

• A. $y=\frac{x}{5}-\frac{1}{2}$
• B. $y=\frac{-x}{5}-\frac{1}{2}$
• C. $y=\frac{-x}{5}+\frac{1}{2}$
• D. $y=-5x-\frac{1}{2}$

Answer 1

The correct option is B $y=\frac{-x}{5}-\frac{1}{2}$

Step 1: Find the $y-$ intercept of the line.
As $x=0$, Line is crossing $y$ -axis at the point $(0,-\frac{1}{2})$.
$\therefore y-$ intercept $=-\frac{1}{2}$

Step 2: Find the slope of the line
The given line is perpendicular to another line of slope $5.$
Let the slope of the line is $m_1$ and slope of the perpendicular line is $m_2$
Given, $m_2=5$

Concept: If two line are perpendicular to each other, then product of the slope of both line is $-1.$
$m_1\times m_2=-1$
$m_1\times 5=-1$
$m_1=\frac{-1}{5}$

Step 3: Now, use the slope intercept form of equation of a line.
$y=mx+b$
Where $m$ is the slope and $b$ is the $y$-intercept of the line.
slope$=m=\frac{-1}{5}$,
$y-$ intercept $b=-\frac{1}{2}$
Equation of the line: $y=\frac{-1}{5}\times x-\frac{1}{2}$
$y=\frac{-x}{5}-\frac{1}{2}$
Option (a) is correct.