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

`(x)/(a)+(y)/(b)=1` ...(i)

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

We have, 3a=b.

`(x)/(a)+(y)/(3a)=1` ...(ii)

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

`(1)/(a)+(3)/(3a)=1`

`(1)/(a)+(1)/(a)=1`

`(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

`(x)/(2)+(y)/(6)=1`

Therefore, the equation of the required line in intercept form is
`(x)/(2)+(y)/(6)=1`.