We can write our line as (collecting #y#):
#y=1/4x+1/2#
so that its slope will be the number in front of #x# i.e.:
#"sope"=1/4#
the line passing through our points must have the same slope to be parallel and using the definition of slope:
#"slope"="change in y"/"change in x"=(y_2-y_1)/(x_2-x_1)=(f-0)/(e-1)#
that must be equal to #1/4# to be parallel, so that:
#(f-0)/(e-1)=1/4#
rearranging we get:
#e-1=4f#
#f=(e-1)/4#
#f=e/4-1/4#
so, given a value for #e# we can calculate the corresponding #f# value that will form coordinates of points on a line. The two values will be linearly dependent!!!
For example:
if #e=1# then #f=1/4-1/4=0#
if #e=2# then #f=1/2-1/4=1/4#
....etc.
#e# and #f# can assume infinite values that depends upon each other according to the above relationship.
