The slope of the line passing through #(2,5) and (0,-2)# is
#m= (y_2-y_1)/(x_2-x_1)= (-2-5)/(0-2)=(-7)/-2=7/2#
Let the equation of the line in slope-intercept form be
#y=mx+c or y=7/2x+c# The point (2,5) will satisfy the
equation. #:. 5= 7/2*2+c or c= 5-7= -2# Hence the
equation of the line in slope-intercept form is #y= 7/2x-2#.
and #y# intercept is #c= -2#
The slope of the line #14x-4y-2=0 or 4y=14x-2 # or
# y= 14/4x-2/4 or y=7/2x-1/2 ;# is # m=7/2#
and #y# intercept is #c=-1/2#. Parallel lines have equal slope .
So the line passing through #(2,5) and (0,-2)# is parallel to the
line #14x-4y-2=0#. Since #y# intercept for two lines is different,
they do not coincide. [Ans]
