Question

The equation of the straight line which passes through the point (3, 4) and whose intercept on y-axis is twice that on x-axis, is

• A. 2x – y = 10
• B. x + 2y = 10
• C. 2x + y = 10
• D. None of these

Answer 1

The correct option is C

2x + y = 10

Let the equation of the line be

$\frac{x}{a}+\frac{y}{b}=1......\left(1\right)$

Given: intercept on y-axis = 2 (intercept on x-axis)

i.e., b = 2a

So, equation (1) becomes

$\frac{x}{a}+\frac{y}{2a}=1$

$\Rightarrow 2x+y=2a\dots \dots \left(2\right)$

Since line (2) passes through the point (3, 4)

$\therefore 2\times 3+4=2a\Rightarrow a-5$

Thus, the equation of the required line is

$2x+y=10$