Consider the vertical line #color(magenta)(x=2)#

Clearly #color(magenta)x=2# goes through the point #color(red)(""(2,6))#

and it intersects #color(blue)(-y+4x=3)# at #color(blue)(""(2,5))#

#color(red)(""(2,6))# is vertically #color(brown)(1)# unit **above** #color(blue)(""(2,5))#, the intersection point with #color(blue)(-y+4x=3)#

#color(green)(""(2,4))# is vertically #color(brown)1# unit **below** #color(blue)(""(2,5))#, the intersection point with #color(blue)(-y+4x=3)#

Therefore #color(blue)(-y+4x=3)# bisects the line segment between #color(green)(""(2,4))# and #color(red)(""(2,6))#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Furthermore (as seen in the image below and considering similar triangles)

any point on a line parallel to #color(blue)(-y+4x=3)# through #color(green)(""(2,4))# will provide, together with #color(red)(""(2,6))# a line segment bisected by #color(blue)(-y+4x=3)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)(-y+4x=3)# can be written in slope-intercept form as

#color(white)("XXX")color(blue)(y=4x-3)# with a y-intercept at #color(blue)(""(-3))#

If the line through #color(green)(""(2,4))# parallel to #color(blue)(-y+4x=3)# is #color(brown)(1)# unit vertically below #color(blue)(-y+4x=3)#

it will have a y-intercept at #color(green)(""(-4))#

and therefore a slope-intercept form of

#color(white)("XXX")color(green)(y=4x-4)#