Find the equation of the passing through p(4,6) which is parallel to the line with equation 4x-2y+6=0

Well, a line parallel to another, will have the same slope as the other, therefore, if this line is parallel to 4x-2y+6=0, then it must have the same slope, so, hmmm what is it anyway?

well, let's solve 4x-2y+6=0 for "y".



so, notice, the equation now in slope-intercept form, we can see what its slope is, alrite.  So we're looking for a line whose slope is 2 and goes through 4,6.