Question

Find the equation of a line which is parallel to the line $2x+3y-6=0$ and the sum of the intercepts on the axes is $10$.

• A. $2x+3y=12$
• B. $x+3y=9$
• C. $3x+2y=8$
• D. $2x+3y=8$

Answer 1

The correct option is A $2x+3y=12$

The equation of a line in form of intercepts on coordinate axes is given by, $\frac{x}{a}+\frac{y}{b}=1$

Slope of the line written above is $m=-\frac{b}{a}$

If according to given conditions the line is parallel to line $2x+3y-6=0$, then their slopes must me equal.

Hence $\Rightarrow m=-\frac{b}{a}=-\frac{2}{3}$

$\Rightarrow 2a=3b$

The sum of the intercepts on axes .i.e. $a+b=10$ (Given)

using above two results we can write $a+\frac{2}{3}a=10$

$\Rightarrow a=6$

$\Rightarrow b=4$

Then the equatiuon of line will be $\frac{x}{6}+\frac{y}{4}=1$

$\Rightarrow 2x+3y=12$

Correct answer is $A$