Question

A line passes through the point (3, 4) and cuts off intercepts from the coordinates axes such that their sum is 14. The equation of the line is.

• A. $4 x - 3 y = 24$
• B. $4 x + 3 y = 24$
• C. $3 x - 4 y = 24$
• D. $3 x + 4 y = 24$

Answer 1

Answer: (B)

$4 x + 3 y = 24$

Answer 2

Given $a + b = 14 \Rightarrow a = 14 - b$

Hence the equation of straight line is $\frac { x } { 14 - b } + \frac { y } { b } = 1$.

Also, it passes through $( 3,4 )$

$\therefore$ $\frac { 3 } { 14 - b } + \frac { 4 } { b } = 1 \Rightarrow b = 8$ or 7

Therefore equations are $4 x + 3 y = 24$and $x + y = 7$.

Trick : This question can be checked with the options as the line $4 x + 3 y = 24$passes through (3, 4) and also cuts the intercepts from the axes whose sum is 14.