The intercepts made by a line on the co-ordinate axes are in the ratio $3 : 4$
and passes through $(3, 0)$

3 x + 4 y = 12

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4 x + 3 y = 12

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4 x - 3 y + 12 = 0

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Solution

The correct option is B $4 x + 3 y = 12$
Let the common factor be $k$

The ratio is $3 : 4$

The intersepts are $3 k, 4 k$

The equation is
$\frac{x}{3 k} + \frac{y}{4 k} = 1 4 k x + 3 k y = 12 k^{2} 4 x + 3 y = 12 k$

It passes through $(3, 0)$

$⟹ 4 (3) + 3 (0) = 12 k k = 1$

So the equation is $4 x + 3 y = 12$

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4 x + 3 y = 12

The line 4x - 3y + 12 = 0 meets x-axis at A. Write the co-ordinates of A.

Determine the equation of the line through A and perpendicular to 4x - 3y + 12 = 0.

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