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

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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

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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 

 

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