Reduce 4x-3y-12=0 to the "intercept form" and hence find its intercepts on the axis .

4x-3y -12 = 0

To write the
equation in intercept form we go as below:

 0 = 4x-3y -12 .
Add  3y to both sides

3y =
4x-12

y = (4/3)x -12/4 or y = (4/3)x-3 is the  slope
intercept form. 3/4 = slope and y = -3 is y
intercept.

Double intercept
form:

4x-3y -12 = 0

 Add 12 to
both sides.

4x-3y = 12. Divide by 12 both
sises.

4x/12-3y/12 = 1. Rewrite as
below:

x/(12/4) +y/(12/-3) = 1.
Or

x/3 +y/(-3) = 1. This is the double intercept form of
4x-3y-12 = 0, where x= 3 and y = -3 are the intercept of the line on x and y axis
respectively.

In otherwords, if ax+by+c = 0 is the equation
of the line, then

ax+by = -c
Or

ax/-c +by/-c = 1

x/(-a/c)
+y/(-b/c) = 1. The intercept form of the equation.

Clearly
If you put y = 0, x = -a/c  and if ypou put x =0, then y = -b/c .  So -a/c and -b/c are
the  intercepts of ax+by+c on x and y axis.

Any equation of
the form x/k+y/l = 1 has the  x intercept k and y inyercept l.