Question

A line $AB$ makes zero intercepts on x-axis and y-axis and it is perpendicular to another line $CD,3x+4y+6=0.$The equation of line $AB$ is

• A. $y=4$
• B. $4x–3y+8=0$
• C. $4x–3y=0$
• D. $4x–3y+6=0$

Answer 1

The correct option is C

$4x–3y=0$

Finding the equation of the line:

Given $AB$ makes zero intercepts on the x-axis and y-axis.

So it passes through the origin$(0,0).$

$\begin{array}{rcl}Slopeof3x+4y+6& =& 0is-\frac{3}{4}\\ SlopeofAB& =& 4/3\end{array}$

Required equation of line passing through origin and slope m is

$\begin{array}{rcl}y& =& \frac{4}{3}x\mathit{y}\mathbf{=}\mathit{m}\mathit{x}\\ 3y–4x& =& 0\\ 4x–3y& =& 0\end{array}$

Hence, option C is the correct answer.