Question

3. 'a' and 'b' are the intercepts made
by a straight-line with the co-
ordinate axes. If 3a = b and the line
pass through the point (1, 3), find
the equation of the line.​

Answer 1

Given:

'a' and 'b' are the intercepts made  by a straight-line with the co- ordinate axes.

3a = b and the line  pass through the point (1, 3).

To find:

The equation of the line.

Solution:

The intercept form of a line is

$\dfrac{x}{a}+\dfrac{y}{b}=1$         ...(i)

where, a is x-intercept and b is y-intercept.

We have, 3a=b.

$\dfrac{x}{a}+\dfrac{y}{3a}=1$           ...(ii)

The line  pass through the point (1, 3). So, putting x=1 and y=3, we get

$\dfrac{1}{a}+\dfrac{3}{3a}=1$

$\dfrac{1}{a}+\dfrac{1}{a}=1$

$\dfrac{2}{a}=1$

Multiply both sides by a.

$2=a$

The value of a is 2. So, x-intercept is 2.

Putting a=2 in $b=3a$, we get

$b=3(2)$

$b=6$

The value of b is 6. So, y-intercept is 6.

Putting a=2 and b=6 in (i), we get

$\dfrac{x}{2}+\dfrac{y}{6}=1$

Therefore, the equation of the required line in intercept form is $\dfrac{x}{2}+\dfrac{y}{6}=1$.