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9. straight line — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS9. straight line1 Mark
MCQ
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
    $4x - 3y = 24$
  • ✓
    $4x + 3y = 24$
  • C
    $3x - 4y = 24$
  • D
    $3x + 4y = 24$
✓

Answer

Correct option: B.
$4x + 3y = 24$
b
(b) 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 $4x + 3y = 24$ and $x + y = 7$.

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

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