Question

Give the equation of two lines passing through (2,-3). How many more such lines are there and why?

Answer 1

infinite lines can be drawn from one point .because one point no give fixed slope e.g possibility of slope is infinity hence lines can be drawn infinity.

let m is the slope of lines then ,
(y+3)=m (x-2)
y+3=mx-2m
mx-y=3+2m
hence this is family of equation which passes through (2,-3)
now ,
put m=1
x-y=5
m=2
2x-y=7
now equations x-y=5 and 2x-y=7 are two lines which passes through (2,-3)

Answer 2

1st,x+y=-1
2nd,x-y=5
there are infinite such lines passing through that point ,because many lines can pass through a single point.