Question

give the equation of two lines passing through (3,-2). 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)







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Answer 2

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)