Question

Find the equation of a straight line passing through 1, - 4 and has intercepts which are in the ratio 2: 5

Answer 1

Answer:

The equation of the line is $5x+2y=3$

Step-by-step explanation:

Let the common ratio be t

Since the intercepts are in the ratio 2:5

Therefore the intercept on the x-axis will be 2t and the intercept on the y-axis will be 5t

The equation of line in intercept form is

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

$\implies \frac{x}{2t}+\frac{y}{5t}=1$

Since this line passes through the point $(-1,4)$

Therefore this point will satisfy the equation of the line

Thus,

$\frac{-1}{2t}+\frac{4}{5t}=1$

$\implies \frac{-5+8}{10t}=1$

$\implies \frac{3}{10t}=1$

$\implies t=\frac{3}{10}$

Thus the equation of the line is

$\implies \frac{x}{2}+\frac{y}{5}=t$

or, $\frac{x}{2}+\frac{y}{5}=\frac{3}{10}$

or, $5x+2y=3$

Hope this helps.

Answer 2

Answer:

Step-by-step explanation: