Question 12728
Your first question, a line parallel to y = 3x + 5 passing through (1,4)
If two lines are parallel they have the same slope.
We know we want our line to have the form y = mx + b.
We know our slope HAS to be 3 becasue the lines are parallel
So now we have y = 3x + b use your point to solve for b
{{{ y = 3x + b }}} Substitute
{{{4 = 3(1) + b }}} Multiply
{{{ 4 = 3 + b }}} Subtract 3 from both sides
{{{ 1 = b }}}
So we know our slope is 3 and y intercept is 1 so 
y = 3x + 1 is parallel to y = 3x + 5
<P>
Your next question, a line perpendicular to y = 6x - 3 passing through (0,5)
If two lines are perpendicular thier slopes are NEGATIVE RECIPROCALS
We know we want our line to have the form y = mx + b
We know our slope for our Perpendicular line is ( -1/6 )
So now we have 
{{{ y = (-1/6)x + b }}} Using your point ( 0,5 ) to solve for b
{{{ 5 = (-1/6)(0) + b }}} Simplify
{{{ 5 = b }}}
We know our slope is ( -1/6 ) and our y intercept is 5 so
y = ( -1/6 )x + 5 is Perpendicular to y = 6x - 3