Question

1.find the area of a triangle formed by the line 2x-4y-7=0 with coordinates axis 
2.find the equation of a line passing through one point (0,5) and whose slope is 7/3
3.find the equation of the line that cuts off intercept a and b on the x and y axis such that a+b=3 and ab = 2

Answer 1

2.    (y- y1)=m(x-x1)
y-5=7/3(x-0)
3(y-5)=3(x-0)
3y-15=3x
y=3/3x+15/3
y=x+5

Answer 2

if x=0
2(0)-4y-7=0
4y+7=0
y=-7/4
if y=0 then 
2x-4(0)-7=0
2x=7 
x=7/2
area of triangle = 1/2 x base x height 
                         = 1/2 x 7/4 x 7/4 
                         = 49/16 sq units 

2.........
(0,5)  slope = 7/3
y-y₁=m(x-x₁)
y₁=5, m=7/3 , x₁ =0
y-5 =7/3 (x-0)
3(y-5) =3 (7/3)(x-0)
3y-15=7x-0
y=x+5

3...............
a+b=3
ab=2
a+b=3
a=3-b
ab=2
=a=2/b
2+b²-3b=0
b²-2b-b+2=0
b(b-2)-1(b-2)=0
(b-2)=0,(b-1)=0
b=2 ,b=1 is nothing but a=1