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Maths-

General

Easy

Question

A line make zero intercepts on x – axis and y – axis and it is perpendicular to the line 3x +4y+ 6 = 0 then its equation is

y = x
4x – 3y = 0
4x – 3y + 8 = 0
4x – 3y + 6 = 0

hint Hint:

Assume the equation of line is $y equals m x plus c$ . It is given that y- intercept is zero so $c equals 0$ . When two lines are perpendicular the product of their slopes is $negative 1$

The correct answer is: 4x – 3y = 0

Let the equation of the line is $y equals m x plus c$
Step1: Line making zero intercept on the x and y axis.
Since the line is making is making zero intercept with y- axis then $c equals 0$
Step2: Line perpendicular to $3 x space plus 4 y plus space 6 space equals space 0$ .
When two lines are perpendicular the product of their slopes is equal to $negative 1$ .
The slope of a line $a x plus b y plus c equals 0$ is given by $fraction numerator negative b over denominator a end fraction$ . Therefore the slope of the given line is $fraction numerator negative 4 over denominator 3 end fraction$
Slope of line to find is $m$ .
Then according to the property of perpendicular lines
$m cross times open parentheses fraction numerator negative 4 over denominator 3 end fraction close parentheses space equals space minus 1$
=> $m space equals space 3 over 4$
Therefore the equation of the line will be $y equals space m x plus c space$ where $c equals 0$ and $m equals 3 over 4$
=> $y equals 4 over 3 x$ or $4 x minus 3 y equals 0$

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