Find the equation of the line that passes through (3,4) and the sum of it's intercepts on the axis is 14.

The equation for the line
is:

y-y1 = m (x-x1)

We have
the point (3,4) psses through the line,

==> y-4 =
m(x-3)

==> y = mx - 3m +
4

==> y - mx = -3m +
4

Divide by -3m +
4:

==> y/(-3m+4) + x/[(-3m+4)/-m] =
1

==> y intercept a =
-3m+4

==> x intercept b =
(-3m+4)/-m

But we know that a+ b =
14

==> -3m + 4 + (-3m+4)/-m =
14

==> -3m + 4 + 3 - 4/m =
14

==> -3m^2 + 7m - 4 =
14m

==> -3m^2 - 7m - 4 =
0

==> m1= [7+ sqrt(49-48)]/-6 = [7+1]/-6 = -8/6=
-4/3

==> m2= [7-1]/-6= 6/-6 =
-1

==> we have two
solutions:

m= -4/3:

==>
y-4 = (-4/3)(x-3)

==> y= (-4/3)x +
8

m= -1:

==> y-4 =
(-1)(x-3)

==> y= -x +7