Question

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

Answer 1

Consider given that,

Y-axis twice as long as that on the x-axis.

Then, let the points be $(a,2a)$

Now, we know that the equation of straight line is

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

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

$2x+y=2a$ ……. (1)

And given point $(x,y)=(3,4)$ lies the line

Then,

$2\times 3+4=2a$

$2a=10$

$a=5$

By equation (1)

$2x+y=2\times 5$

$2x+y=10$

Or

$\frac{x}{5}+\frac{y}{10}=1$

Hence, it is complete solution.