I am not sure that it is what you need but I'll try.

In an equation the left side has to be equal to the right side, so you can choose a value of #x# and evaluate the correspondent value of #y# but the two sides must remain equal. Now if you choose #x=0# in your equation #y# has to be equal to zero.

For example, consider the equation #y=3x# this equation has #oo# solutions depending on the value of #x# you choose.

Try to substitute #x=0#, you'll get:

#y=3*0=0#

So for #x=0 -> y=0#

Graphically, a linear equation is represented by a straight line, and in the case of #y=3x# is a straight line that passes through the origin (which has coordinates #x=0#, #y=0#).

Try by yourself using #y=3x#, choose various values for #x# (say #-2,-1,0,1,2#) and plot the values obtained as points of coordinates #x and y# on a Cartesian coordinate system.