Question

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

• A. 2x – y = 10
• B. x + 2y = 10
• C. 2x + y = 10
• D. 3x-4y+7=0

Answer 1

The correct option is C

2x + y = 10

Let the equation of the line be $\frac{x}{a}+\frac{y}{b}=1$ , where a and b are the x and y intercepts respectively. ......(1)

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

i.e., b = 2a

So, equation (1) becomes $\frac{x}{a}+\frac{y}{2a}=1$

or 2x + y = 2a …… (2)

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