Question

A line makes positive intercepts on coordinate axes whose sum is 7 and it passes through (-3,7) find its equation.​

Answer 1

Equation of the line in the intercept form is

x/a+y/b=1-----(1)

It is given that the sum of the intercepts is 14.

(i.e) a+b=14

or b=14−a

Substituting this in equivalent (1) we get.

x/a+y/(14−a)=1

(i.e) x(14−a)+y(a)=a(14−a)

This line passes through the point (3, 4)

∴3(14−a)+4(a)=a(14−a)

⇒42−3a+4a=14a−a2

(i.e) a2−13a+42=0

On factorizing this we get,

(a−6)(a−7)=0

∴a=6 or a=7

Step 3

Case (i)

If a=6 then b=8

Hence the equation of the line is

x6+y8=1

(i.e) 8x+6y=48

or 4x+3y=24

Step 4

Case (ii)

If a=7 then b=7

Hence the equation of the line is

x7+y7=1

⇒x+y=7

Answer 2

Answer:

PLEASE REFER TO THE ATTACHMENT!!