The equation of line joining #x_1,y_1)# and #x_2,y_2)# is given by
#(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)#
while equation in pint slope form is of the type #y=mx+c#
Hence equation of line joining #(0,2)# and #(4,5)# is
#(y-2)/(5-2)=(x-0)/(4-0)#
or #(y-2)/3=x/4# or #4y-8=3x# or #4y=3x+8# and
in point slope form it is #y=3/4x+2#
and equation of line joining #(0,0)# and #(4,5)# is
#(y-0)/(5-0)=(x-0)/(4-0)#
or #y/5=x/4# or #4y=5x# and
in point slope form it is #y=5/4x#
For equation of line joining #(0,0)# and #(0,2)#, as #x_2-x_1=0# i.e. #x_2=x_1#, the denominator becomes zero and it is not possible to get equation. Similar would be the case if #y_2-y_1=0#. In such cases as ordinates or abscissa are equal, we will have equations as #y=a# or #x=b#.
Here, we have to find the equation of line joining #(0,0)# and #(0,2)#. As we have common abscissa, the equation is
#x=0#
