Question

Find an equation of a straight line which intersepts whose sum is 5 and product is 6

Answer 1

y=ax+b is the standard linear equation.

The y intercept is b and the x intercept is -b/a.

So b-b/a=5 and -b^2/a=6. Multiply each equation through by

a: ab-b=5a and b^2=-6a.

So b(a-1)=5a and b=5a/(a-1).

Substitute this in the other equation:

25a^2/(a-1)^2=-6a.

Divide through by a: 25a/(a-1)^2=-6.

Multiply through by (a-1)^2: 25a=-6(a-1)^2=-6a^2+12a-6. This can be written: 6a^2+13a+6=0=(3a+2)(2a+3)=0. So a=-2/3 or -3/2. And b=2 or 3.

The linear equations are y=-2x/3+2 and y=-3x/2+3. These can be written 3y+2x=6 and 2y+3x=6.