Question

Find equation of straight line passing through the point (2,5)and with ratio of x intercept to Y intercept is 2:5

Answer 1

Answer:

Step-by-step explanation:

Let x-intercept and y-intercept of the line be 'a' and 'b'

It is given that a : b = 2 : 5

$\sf{\implies\,\dfrac{a}{b}=\dfrac{2}{5}}$

$\sf{\implies\,a=\dfrac{2b}{5}\,\,\,\,\,\,\,\,\,\,...(1)}$

We know, equation of a line in intercept form is given by

$\tt{\dfrac{x}{a}+\dfrac{y}{b}=1}$

where 'a' and 'b' are x and y-intercepts

So, the equation of the line

$\tt{\dfrac{x}{\dfrac{2b}{5}}+\dfrac{y}{b}=1}$

$\tt{\implies\dfrac{5x}{2b}+\dfrac{y}{b}=1}$

Now, the line passes through (2,5)

So,

$\tt{\implies\dfrac{5\times2}{2b}+\dfrac{5}{b}=1}$

$\tt{\implies\dfrac{5}{b}+\dfrac{5}{b}=1}$

$\tt{\implies\dfrac{10}{b}=1}$

$\tt{\implies\,b=10}$

So,

$\tt{\implies\,a=\dfrac{2\times10}{5}}$

$\tt{\implies\,a=2\times2}$

$\tt{\implies\,a=4}$

Hence, the required equation of the straight line is

$\sf{\dfrac{x}{4}+\dfrac{y}{10}=1}$

$\sf{\implies5x+2y=20}$