Divide both sides by -3, and replace with
. Then
Factorize the quadratic in to get
which in turn means
But for all real
, so we can ignore the first solution. This leaves us with
If we allow for any complex solution, then we can continue with the solution we ignored:
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
...(i)
where, a is x-intercept and b is y-intercept.
We have, 3a=b.
...(ii)
The line pass through the point (1, 3). So, putting x=1 and y=3, we get
Multiply both sides by a.
The value of a is 2. So, x-intercept is 2.
Putting a=2 in , we get
The value of b is 6. So, y-intercept is 6.
Putting a=2 and b=6 in (i), we get
Therefore, the equation of the required line in intercept form is .