Question

How many lines can pass through the point (-1,3). determine the equations of any two of these lines.

Answer 1

in one infinite number of lines can be passs .
general equation of that lines is
(y -3) = m( x +1)

y -3 = mx + m

y = mx + m +3

now ,
y = mx +( m+3) is general equation of line which passing through (-1, 3)

put m = 1
y = x +4
put m = 2
y = 2x + 5

hence , y =x +4 and y = 2x +5 two lines which passing through (-1, 3)

Answer 2

Hi friend,
Infinite number of lines may pass through a given point (x1,y1).
Equation of lines passing through (x1,y1) is given by y-y1=m(x-x1)
Here, x1=-1 and y1=3 so equation of line will be y-3=m(x+1)
                                                                             y-3=mx+m
 So if m=1 equation of line is y-3=x+1
      if m=2 equation of line is y-3=2x+2⇒ 2x-y+5=0.